\batchmode
%
\documentclass[12pt,letterpaper,oneside,onecolumn]{article}
\makeatletter
\usepackage[]{fontenc}
\usepackage[dvips]{epsfig}


\makeatletter












\makeatother


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{
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\makeatother
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\def\lthtmltypeout#1{{\let\protect\string\immediate\write\lthtmlwrite{#1}}}%
\newbox\sizebox
\begin{document}
\pagestyle{empty}
\setcounter{secnumdepth}{3}
\setcounter{tocdepth}{3}
{\newpage
\clearpage
\samepage \( G(r^{i},r'^{i})=\sum _{n,m}g_{nm}(z,r'^{i})sin(k_{xn}x)sin(k_{ym}y) \)
}

{\newpage
\clearpage
\samepage \( k_{xn}=\frac{n\pi }{a} \)
}

{\newpage
\clearpage
\samepage \( k_{ym}=\frac{m\pi }{b} \)
}

{\newpage
\clearpage
\samepage \( g_{nm} \)
}

{\newpage
\clearpage
\samepage \( (\frac{d^{2}}{dz^{2}}-k_{z,nm}^{2})g_{nm}(z,r'^{i})=-\frac{4}{ab}4\pi \delta (z-z')sin(k_{xn}x')sin(k_{ym}y') \)
}

{\newpage
\clearpage
\samepage \( g_{nm}=h_{nm}(z,z')sin(k_{xn}x')sin(k_{ym}y') \)
}

{\newpage
\clearpage
\samepage \( (\frac{d^{2}}{dz^{2}}-k_{z,nm}^{2})h_{nm}(z,z')=-\frac{1}{ab}16\pi \delta (z-z') \)
}

{\newpage
\clearpage
\samepage \( Asinh(k_{z,nm}z) \)
}

{\newpage
\clearpage
\samepage \( z<z' \)
}

{\newpage
\clearpage
\samepage \( Bsinh(k_{z,nm}(c-z)) \)
}

{\newpage
\clearpage
\samepage \( z>z' \)
}

{\newpage
\clearpage
\samepage \( h_{nm}=Csinh(k_{z,nm}z_{min})sinh(k_{z,nm}(c-z_{max}) \)
}

{\newpage
\clearpage
\samepage \( G(r^{i},r'^{i})=\frac{16\pi }{ab}\sum _{n,m}sin(k_{xn}x')sin(k_{xn}x)sin(k_{ym}y')sin(k_{ym}y)*\frac{1}{k_{z,nm}sinh(k_{z,nm}c)} \)
}

{\newpage
\clearpage
\samepage \( *sinh(k_{z,nm}z_{min})sinh(k_{z,nm}(c-z_{max}) \)
}

{\newpage
\clearpage
\samepage \( \psi _{lmn}(r^{i})=\frac{8}{abc}sin(k_{xl}x)sin(k_{ym}y)sin(k_{zn}z) \)
}

{\newpage
\clearpage
\samepage \( k_{xl}=\frac{l\pi }{a} \)
}

{\newpage
\clearpage
\samepage \( G(r^{i},r'^{i})=\frac{32}{abc\pi ^{2}}\sum _{l,n,m}\frac{1}{(\frac{l}{a})^{2}+(\frac{m}{b})^{2}+(\frac{n}{c})^{2}}\psi _{lmn}(r'^{i})\psi _{lmn}(r^{i}) \)
}

{\newpage
\clearpage
\samepage \( sinh(k_{z,lm}z_{min})sinh(k_{z,lm}(c-z))\frac{1}{k_{z,lm}sinh(k_{z,lm}c)}=\frac{2}{c}\sum _{n=1}^{\infty }\frac{sin(\frac{n\pi }{c}z)sin(\frac{n\pi }{c}z')}{k_{z,lm}^{2}+\frac{n^{2}\pi ^{2}}{c^{2}}} \)
}


\end{document}
