This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013) (format=pdflatex 2014.2.4) 11 AUG 2016 14:35 entering extended mode \write18 enabled. %&-line parsing enabled. **ex_3240 (./ex_3240.tex LaTeX2e <2011/06/27> Babel <3.9f> and hyphenation patterns for 62 languages loaded. ! Undefined control sequence. l.2 \sect {Bose gas in a uniform gravitational field} ? q OK, entering \batchmode... ! LaTeX Error: Missing \begin{document}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.2 \sect{B ose gas in a uniform gravitational field} You're in trouble here. Try typing to proceed. If that doesn't work, type X to quit. Missing character: There is no B in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no g in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no g in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no v in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no d in font nullfont! Overfull \hbox (20.0pt too wide) in paragraph at lines 2--3 [] [] ! Undefined control sequence. l.6 \Dn The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: Missing \begin{document}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.8 C onsider an ideal Bose gas of particles of mass $m$ in a uniform gravita... You're in trouble here. Try typing to proceed. If that doesn't work, type X to quit. Missing character: There is no C in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no B in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no g in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no s in font nullfont! LaTeX Font Info: External font `cmex10' loaded for size (Font) <7> on input line 8. LaTeX Font Info: External font `cmex10' loaded for size (Font) <5> on input line 8. Missing character: There is no i in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no g in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no v in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no . in font nullfont! Overfull \hbox (20.0pt too wide) in paragraph at lines 8--9 [] [] Overfull \hbox (8.78014pt too wide) in paragraph at lines 8--9 \OML/cmm/m/it/10 m$ [] Overfull \hbox (5.12846pt too wide) in paragraph at lines 8--9 \OML/cmm/m/it/10 g$ [] ! Undefined control sequence. l.10 \Dn The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: Missing \begin{document}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.12 ( 1) Show that the phenomenon of Bose-Einstein condensation in this gas ... You're in trouble here. Try typing to proceed. If that doesn't work, type X to quit. Missing character: There is no ( in font nullfont! Missing character: There is no 1 in font nullfont! Missing character: There is no ) in font nullfont! Missing character: There is no S in font nullfont! Missing character: There is no h in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no w in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no h in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no h in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no h in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no B in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no - in font nullfont! Missing character: There is no E in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no h in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no g in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no g in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no v in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no b in font nullfont! Missing character: There is no y in font nullfont! ! Undefined control sequence. l.14 \beq The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Missing character: There is no T in font nullfont! ! Missing $ inserted. $ l.15 T_ c \approx T_c^0 \left[ 1+ \dfrac{8}{9} \dfrac{1}{\zeta(3/2)} \sqrt{ ... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Undefined control sequence. l.15 T_c \approx T_c^0 \left[ 1+ \dfrac {8}{9} \dfrac{1}{\zeta(3/2)} \sqrt{ ... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.15 ...approx T_c^0 \left[ 1+ \dfrac{8}{9} \dfrac {1}{\zeta(3/2)} \sqrt{ \d... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.15 ...8}{9} \dfrac{1}{\zeta(3/2)} \sqrt{ \dfrac {\pi mgL}{kT_c^0}}\right] The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.16 \eeq The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Missing character: There is no L in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no g in font nullfont! Missing character: There is no L in font nullfont! ! Missing $ inserted. $ l.18 ...$L$ is the height of the tank and $mgL \ll kT_c^0 $, where $T_c^0\eq... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. Missing character: There is no , in font nullfont! Missing character: There is no w in font nullfont! Missing character: There is no h in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no e in font nullfont! ! Undefined control sequence. l.18 ...and $mgL \ll kT_c^0 $, where $T_c^0\equivT _c^0(g=0)$. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Double subscript. l.18 ...nd $mgL \ll kT_c^0 $, where $T_c^0\equivT_ c^0(g=0)$. I treat `x_1_2' essentially like `x_1{}_2'. Missing character: There is no . in font nullfont! Overfull \hbox (20.0pt too wide) in paragraph at lines 12--19 [] [] Overfull \hbox (9.9175pt too wide) in paragraph at lines 12--19 \OML/cmm/m/it/10 T[]$ [] Overfull \hbox (14.62926pt too wide) in paragraph at lines 12--19 [] \OMS/cmsy/m/n/10 ^^Y [] Overfull \hbox (278.20146pt too wide) in paragraph at lines 12--19 \OML/cmm/m/it/10 T[] [] where$$istheheightofthetankand$ [] Overfull \hbox (10.00002pt too wide) in paragraph at lines 12--19 \OMS/cmsy/m/n/10 ^^\ [] Overfull \hbox (17.23962pt too wide) in paragraph at lines 12--19 \OML/cmm/m/it/10 kT[]$ [] Overfull \hbox (35.77779pt too wide) in paragraph at lines 12--19 \OML/cmm/m/it/10 T[][]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 g \OT1/cmr/m/n/10 = [] Overfull \hbox (8.88892pt too wide) in paragraph at lines 12--19 \OT1/cmr/m/n/10 0)$ [] ! Undefined control sequence. l.20 \Dn The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: Missing \begin{document}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.22 ( 2) Show that the condensation is accompanied by a discontinuity in the... You're in trouble here. Try typing to proceed. If that doesn't work, type X to quit. Missing character: There is no ( in font nullfont! Missing character: There is no 2 in font nullfont! Missing character: There is no ) in font nullfont! Missing character: There is no S in font nullfont! Missing character: There is no h in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no w in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no h in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no h in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no b in font nullfont! Missing character: There is no y in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no y in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no h in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no h in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no h in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no g in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no : in font nullfont! ! Undefined control sequence. l.24 \beq The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Missing character: There is no ( in font nullfont! ! Missing $ inserted. $ l.25 (\Delta C_V)_{T=T_c}\approx -\dfrac{9}{8\pi}\zeta(3/2)Nk\sqrt{\dfrac{\p... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Undefined control sequence. l.25 (\Delta C_V)_{T=T_c}\approx -\dfrac {9}{8\pi}\zeta(3/2)Nk\sqrt{\dfrac{\p... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.25 ...x -\dfrac{9}{8\pi}\zeta(3/2)Nk\sqrt{\dfrac {\pi mgL}{kT_c^0}} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.26 \eeq The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.27 I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. Overfull \hbox (20.0pt too wide) in paragraph at lines 22--27 [] [] Overfull \hbox (57.77843pt too wide) in paragraph at lines 22--27 \OT1/cmr/m/n/10 ^^A\OML/cmm/m/it/10 C[]\OT1/cmr/m/n/10 )[] \OMS/cmsy/m/n/10 ^^Y [] Overfull \hbox (120.38626pt too wide) in paragraph at lines 22--27 \OMS/cmsy/m/n/10 ^^@\OT1/cmr/m/n/10 9[]\OML/cmm/m/it/10 ^^P\OT1/cmr/m/n/10 (3\O ML/cmm/m/it/10 =\OT1/cmr/m/n/10 2)\OML/cmm/m/it/10 Nk[]$ [] ! Undefined control sequence. l.28 \Dn The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: Missing \begin{document}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.30 \textbf{Hint:} note the following expansion of the polylogarithmic func... You're in trouble here. Try typing to proceed. If that doesn't work, type X to quit. Missing character: There is no n in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no h in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no w in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no g in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no x in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no h in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no y in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no g in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no h in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no : in font nullfont! ! Undefined control sequence. l.32 \beq The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Missing character: There is no L in font nullfont! Missing character: There is no i in font nullfont! ! Missing $ inserted. $ l.33 Li_ {\nu}(\eexp{-\alpha})=\dfrac{\Gamma(1-\nu)}{\alpha^{1-\nu}}+\sum_{i=... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Undefined control sequence. l.33 Li_{\nu}(\eexp {-\alpha})=\dfrac{\Gamma(1-\nu)}{\alpha^{1-\nu}}+\sum_{i=... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.33 Li_{\nu}(\eexp{-\alpha})=\dfrac {\Gamma(1-\nu)}{\alpha^{1-\nu}}+\sum_{i=... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.33 ...\alpha^{1-\nu}}+\sum_{i=0}^{\infty}{\dfrac {(-1)^i}{i}\zeta(\nu-i)\al... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.34 \eeq The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.35 I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. Overfull \hbox (45.93042pt too wide) in paragraph at lines 30--35 []\OT1/cmr/bx/n/10 Hint: [] Overfull \hbox (37.52087pt too wide) in paragraph at lines 30--35 []\OT1/cmr/m/n/10 ([]) = [] Overfull \hbox (66.25006pt too wide) in paragraph at lines 30--35 [][] \OT1/cmr/m/n/10 + [] Overfull \hbox (96.9042pt too wide) in paragraph at lines 30--35 [][] []$ [] ) ! Emergency stop. <*> ex_3240 *** (job aborted, no legal \end found) Here is how much of TeX's memory you used: 10 strings out of 493392 179 string characters out of 6143120 51413 words of memory out of 5000000 3537 multiletter control sequences out of 15000+600000 3948 words of font info for 15 fonts, out of 8000000 for 9000 953 hyphenation exceptions out of 8191 18i,4n,12p,131b,67s stack positions out of 5000i,500n,10000p,200000b,80000s ! ==> Fatal error occurred, no output PDF file produced!