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$key = q/{_inline}$Lambda${_inline}/;
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$key = q/{_inline}$G(Lambda)=Lambda${_inline}/;
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$key = q/{_inline}$q_ngeF_n${_inline}/;
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$key = q/{_inline}$12${_inline}/;
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$key = q/{_inline}$A^TA${_inline}/;
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$key = q/{_inline}$e^2piix${_inline}/;
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$key = q/{_inline}$e^pi^2(6ln2)${_inline}/;
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$key = q/{_inline}$)${_inline}/;
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$key = q/{_inline}$e=2+[1,2,1,1,4,1,1,6,1,1,8,ldots]${_inline}/;
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$key = q/{_inline}$gamma_k;SPM_gt;1tau${_inline}/;
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$key = q/{_inline}$n_0+[n_1,n_2,n_3,ldots]${_inline}/;
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$key = q/{_inline}$r_m=0${_inline}/;
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$key = q/{_inline}$e_k+m=z_k+m-x_k+m${_inline}/;
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$key = q/{_inline}$[a_1,a_2,a_3,ldots]${_inline}/;
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$key = q/{_inline}$tau${_inline}/;
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$key = q/{_inline}$gamma_0=0.3${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img166.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img166.gif"></A>'; 
$key = q/{_inline}$lambda${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img140.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img140.gif"></A>'; 
$key = q/{_inline}$gamma=[n_1,n_2,n_3,ldots]${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img54.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img54.gif"></A>'; 
$key = q/{_inline}$z_k+mz_k+m+1${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img232.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img232.gif"></A>'; 
$key = q/{_inline}$y_0${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img238.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img238.gif"></A>'; 
$key = q/{_inline}$[1,1,1,1,ldots]${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img63.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img63.gif"></A>'; 
$key = q/{_inline}$z_k+m=[a_k+m+1,a_k+m+2,ldots,a_k+n+1]${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img218.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img218.gif"></A>'; 
$key = q/{_inline}$tau^4${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img132.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img132.gif"></A>'; 
$key = q/{_inline}$a_3${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img191.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img191.gif"></A>'; 
$key = q/{_inline}$km${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img30.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img30.gif"></A>'; 
$key = q/{_inline}$pi${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img254.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img254.gif"></A>'; 
$key = q/{_inline}$a_1${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img189.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img189.gif"></A>'; 
$key = q/{_inline}$z_ktoy_k${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img236.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img236.gif"></A>'; 
$key = q/{_inline}$O(logvarepsilon)${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img80.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img80.gif"></A>'; 
$key = q/{_inline}$gamma_kcdotgamma_k+1=gamma_k+1(n_k+1+gamma_k+1)=1-n_k+1gamma_kle1-gamma_k;SPM_lt;1-1tau=1tau^2${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img130.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img130.gif"></A>'; 
$key = q/{_inline}$gamma_k=1(n_k+1+gamma_k+1)${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img125.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img125.gif"></A>'; 
$key = q/{_inline}$-infty${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img274.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img274.gif"></A>'; 
$key = q/{_inline}${1,0,12}${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img92.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img92.gif"></A>'; 
$key = q/{_inline}$O(b^k)${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img324.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img324.gif"></A>'; 
$key = q/{_inline}$gamma_k+1${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img121.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img121.gif"></A>'; 
$key = q/{_inline}$gamma_3=0.3=gamma_0${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img163.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img163.gif"></A>'; 
$key = q/{_inline}$ln2${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img253.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img253.gif"></A>'; 
$key = q/{_inline}$xtof(x)${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img290.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img290.gif"></A>'; 
$key = q/{_inline}$[ldots,1,1,1,ldots]${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img315.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img315.gif"></A>'; 
$key = q/{_inline}$m=1,2,ldots,n${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img219.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img219.gif"></A>'; 
$key = q/{_inline}$ldots${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img68.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img68.gif"></A>'; 
$key = q/{_inline}$.010201212ldots${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img328.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img328.gif"></A>'; 
$key = q/{_inline}$varepsilon;SPM_gt;0${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img260.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img260.gif"></A>'; 
$key = q/{_inline}$r_k+1=r_k-1rmmodr_k${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img270.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img270.gif"></A>'; 
$key = q/{_inline}$G(gamma_1)=gamma_2=[n_3,n_4,n_5,ldots]${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img45.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img45.gif"></A>'; 
$key = q/{_inline}$x_2${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img185.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img185.gif"></A>'; 
$key = q/{_inline}$(0,1)${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img115.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img115.gif"></A>'; 
$key = q/{displaymath}lambda=lim_ntoinftyfrac1nsum_k=0^nln(|G'(gamma_k)|){displaymath}/;
$cached_env_img{$key} ='<A HREF=/cgi-bin/organics/nmpform?mfname=img296.mpl><IMG ALIGN=RIGHT BORDER=0 SRC="../gif/maple/maple296.gif"> </A><A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img296.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img296.gif"></A>'; 
$key = q/{_inline}$G(1)=G(12)=0${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img94.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img94.gif"></A>'; 
$key = q/{_inline}$r_m-1${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img273.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img273.gif"></A>'; 
$key = q/{_inline}$x_0${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img197.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img197.gif"></A>'; 
$key = q/{_inline}$O(1)${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img4.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img4.gif"></A>'; 
$key = q/{_inline}$pn=[a_1,a_2,ldots,a_i]${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img82.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img82.gif"></A>'; 
$key = q/{_inline}$tau=1+[1,1,1,1,ldots]${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img61.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img61.gif"></A>'; 
$key = q/{_inline}$z_k-y_k${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img223.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img223.gif"></A>'; 
$key = q/{_inline}$gamma_k${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img123.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img123.gif"></A>'; 
$key = q/{_inline}$2^n${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img138.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img138.gif"></A>'; 
$key = q/{_inline}$F_n${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img203.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img203.gif"></A>'; 
$key = q/{_inline}$0.2${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img175.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img175.gif"></A>'; 
$key = q/{_inline}$pn${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img77.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img77.gif"></A>'; 
$key = q/{_inline}$n_2${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img67.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img67.gif"></A>'; 
$key = q/{_inline}$mu(A)=frac1ln(2)int_Adx(1+x)${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img307.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img307.gif"></A>'; 
$key = q/{_inline}$n_0${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img8.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img8.gif"></A>'; 
$key = q/{_inline}$2lntau${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img136.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img136.gif"></A>'; 
$key = q/{_inline}$0.73${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img172.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img172.gif"></A>'; 
$key = q/{_inline}$z_k${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img227.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img227.gif"></A>'; 
$key = q/{_inline}$z_k+m${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img231.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img231.gif"></A>'; 
$key = q/{displaymath}p_nq_n=[a_k+1,a_k+2,a_k+3,ldots,a_k+n]{displaymath}/;
$cached_env_img{$key} ='<A HREF=/cgi-bin/organics/nmpform?mfname=img200.mpl><IMG ALIGN=RIGHT BORDER=0 SRC="../gif/maple/maple200.gif"> </A><A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img200.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img200.gif"></A>'; 
$key = q/{_inline}$O(rmlog(min(k,m)))${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img31.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img31.gif"></A>'; 
$key = q/{_inline}$G(gamma_0)=gamma_1=[n_2,n_3,n_4,ldots],${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img44.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img44.gif"></A>'; 
$key = q/{_inline}$1gamma_k^2gamma_k+1^2${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img131.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img131.gif"></A>'; 
$key = q/{_inline}$gamma_0${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img298.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img298.gif"></A>'; 
$key = q/{_inline}$delta${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img152.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img152.gif"></A>'; 
$key = q/{_inline}$lambda(gamma)${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img118.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img118.gif"></A>'; 
$key = q/{_inline}$pi^2(6ln2)${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img256.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img256.gif"></A>'; 
$key = q/{_inline}$omega${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img263.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img263.gif"></A>'; 
$key = q/{_inline}$gamma_k+1=G(gamma_k)${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img297.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img297.gif"></A>'; 
$key = q/{_inline}$gamma_2=0.0000000003${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img162.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img162.gif"></A>'; 
$key = q/{_inline}$prod_i=0^N(1gamma_i^2)${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img117.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img117.gif"></A>'; 
$key = q/{_inline}$gamma_0=[n_1,n_2,n_3,ldots]${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img43.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img43.gif"></A>'; 
$key = q/{_inline}$x_k+n+1${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img215.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img215.gif"></A>'; 
$key = q/{_inline}$1e${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img78.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img78.gif"></A>'; 
$key = q/{_inline}$y_k${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img228.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img228.gif"></A>'; 
$key = q/{_inline}$1n${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img101.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img101.gif"></A>'; 
$key = q/{_inline}$[1,2N,1,1,2(N+1),1,1,ldots]${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img87.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img87.gif"></A>'; 
$key = q/{_inline}$r_1=b${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img269.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img269.gif"></A>'; 
$key = q/{_inline}$1tau${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img64.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img64.gif"></A>'; 
$key = q/{_inline}$[0,1]${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img314.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img314.gif"></A>'; 
$key = q/{_inline}$r_0=a${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img268.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img268.gif"></A>'; 
$key = q/{_inline}$(x_0)${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img317.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img317.gif"></A>'; 
$key = q/{_inline}$x_0,x_1,x_2,x_3,ldots${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img210.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img210.gif"></A>'; 
$key = q/{_inline}$[1,2,1,1,2,1,1,1,1,2,ldots]${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img137.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img137.gif"></A>'; 
$key = q/{_inline}$gamma=n_0+[n_1,n_2,ldots]${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img51.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img51.gif"></A>'; 
$key = q/{_inline}$x^3-3600x^2+120x-2=0${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img95.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img95.gif"></A>'; 
$key = q/{_inline}$gamma_k=0${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img37.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img37.gif"></A>'; 
$key = q/{_inline}$[1,63,17,3]=[1,63,17,2,1]${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img29.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img29.gif"></A>'; 
$key = q/{_inline}$lambda(1tau)=2lntau${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img113.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img113.gif"></A>'; 
$key = q/{_inline}$x=1n${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img38.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img38.gif"></A>'; 
$key = q/{_inline}$e_k+n+1=x_k+n+1a_k+n+1${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img216.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img216.gif"></A>'; 
$key = q/{_inline}$lambda=2.36992${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img174.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img174.gif"></A>'; 
$key = q/{_inline}$G(x)=${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img305.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img305.gif"></A>'; 
$key = q/{_inline}$gamma=[n_1,n_2,ldots,n_k,1,1,1,1,ldots]${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img135.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img135.gif"></A>'; 
$key = q/{_inline}$ln(K)${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img150.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img150.gif"></A>'; 
$key = q/{_inline}$sqrtbfu${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img240.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img240.gif"></A>'; 
$key = q/{_inline}$a_k+n+1${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img214.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img214.gif"></A>'; 
$key = q/{_inline}$x_k${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img316.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img316.gif"></A>'; 
$key = q/{_inline}$(0,1n)${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img308.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img308.gif"></A>'; 
$key = q/{_inline}$|x_m+k-y_n+k|;SPM_lt;e${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img286.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img286.gif"></A>'; 
$key = q/{_inline}$D_f${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img292.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img292.gif"></A>'; 
$key = q/{_inline}$y_k=[a_k+1,a_k+2,a_k+3,ldots]${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img199.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img199.gif"></A>'; 
$key = q/{_inline}$[2N,1,1,2(N+1),1,1,ldots]${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img88.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img88.gif"></A>'; 
$key = q/{_inline}$n_k${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img69.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img69.gif"></A>'; 
$key = q/{_inline}$x_k+1=f(x_k)${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img266.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img266.gif"></A>'; 
$key = q/{_inline}$ln(K)=frac1ln2int_0^1fracln(rmfrac(1x))1+x,dx${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img149.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img149.gif"></A>'; 
$key = q/{_inline}$n_i${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img333.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img333.gif"></A>'; 
$key = q/{_inline}$S(.0102...)=.102...${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img330.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img330.gif"></A>'; 
$key = q/{_inline}$delta_k+n${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img211.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img211.gif"></A>'; 
$key = q/{_inline}$tau^2N${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img119.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img119.gif"></A>'; 
$key = q/{_inline}$=10^-11${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img242.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img242.gif"></A>'; 
$key = q/{_inline}$k=0,1,2,ldots${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img301.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img301.gif"></A>'; 
$key = q/{_inline}$kgeK${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img285.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img285.gif"></A>'; 
$key = q/{_inline}$e${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img261.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img261.gif"></A>'; 
$key = q/{_inline}$mu(A)=mu(f(A))${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img304.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img304.gif"></A>'; 

1;

