# LaTeX2HTML 96.1-d (Mar 10, 1996)
# Associate images original text with physical files.
$key = q/{_inline}$phi_k(vecr)${_inline}/;
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$key = q/{_inline}$r'=vertvecr'vert${_inline}/;
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$key = q/{_inline}$x=costheta${_inline}/;
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';
$key = q/{_inline}$ell=m=0${_inline}/;
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$key = q/{_inline}$gamma_n^(0)=n+2${_inline}/;
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$key = q/{_inline}$gamma_n^(2)=n+3${_inline}/;
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';
$key = q/{_inline}$vecR_k${_inline}/;
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';
$key = q/{_inline}$mathcalY_ell_1^m_1(nabla)F_ell_2^m_2(r)${_inline}/;
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';
$key = q/{_inline}$P_n+k(x)${_inline}/;
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';
$key = q/{_inline}$chi_j${_inline}/;
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';
$key = q/{_inline}$P(r)exp(-alphar^tau)${_inline}/;
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$key = q/{_inline}$chi_j(vecr)=rho_j(r)sigma_j(theta,phi)${_inline}/;
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';
$key = q/{_inline}$rtoinfty${_inline}/;
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$key = q/{_inline}$r_;SPMlt;=min(r,r')${_inline}/;
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$key = q/{_inline}$t_n${_inline}/;
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$key = q/{_inline}$U_Q${_inline}/;
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$key = q/{_inline}$r'_;SPMlt;=min(r',R)${_inline}/;
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$key = q/{_inline}$rho(vecr)${_inline}/;
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$key = q/{_inline}$[![x]!]${_inline}/;
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$key = q/{_inline}$beta=1${_inline}/;
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$key = q/{_inline}$vecrne0${_inline}/;
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';
$key = q/{_inline}$U(vecr)${_inline}/;
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$key = q/{_inline}$tildeP_n(x)=P_n+1(x)${_inline}/;
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$key = q/{_inline}$gamma_ell^(2)=ell+3${_inline}/;
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$key = q/{_inline}$tau=1${_inline}/;
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$key = q/{_inline}$cdot10^1${_inline}/;
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$key = q/{_inline}$cdot10^5${_inline}/;
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$key = q/{eqnarray*}s_4'=lefteqn-displaystylefrac12(x^4,c_4,c_1,c_3,c_2+(-196,c_1^2,c_3,c_4+492,c_4,c_1,c_2^2-300,c_1,c_2,c_3^2),x^3;SPMamp;;SPMamp;mbox+(-c_1,c_2,c_3,c_4-196,c_1,c_3,c_4,c_0+328,c_4,c_1^2,c_2-180,c_1,c_2^2,c_3),x^2+(;SPMamp;;SPMamp;114,c_2,c_3,c_4,c_0-164,c_4,c_1,c_2^2+328,c_4,c_1,c_2,c_0+180,c_1,c_2,c_3^2;SPMamp;;SPMamp;mbox-120,c_1^2,c_2,c_3-114,c_1^2,c_3,c_4)xmbox+60,c_1,c_2^2,c_3-120,c_1,c_2,c_3,c_0;SPMamp;;SPMamp;mbox-114,c_1,c_3,c_4,c_0)c_0leftvruleheight0.47emwidth0emdepth0.47emright.!!(98,x^2,c_4,c_1,c_3,c_0;SPMamp;;SPMamp;mbox+(-164,c_4,c_1,c_2,c_0-57,c_2,c_3,c_4,c_0),x+6,c_1,c_2,c_3,c_4+60,c_1,c_2,c_3,c_0;SPMamp;;SPMamp;mbox+57,c_1,c_3,c_4,c_0){eqnarray*}/;
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$key = q/{_inline}${s_taun}_n=0^infty={s_0,s_tau,s_2tau,dots}${_inline}/;
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';
$key = q/{_inline}$P_n+2(x)${_inline}/;
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';
$key = q/{_inline}$x^ay^bz^c${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$psi_alpha(vecr)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$rho(vecr')ne0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$B_n(x)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Q_ell^m${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$s_2N'${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tildeQ_n(x)=Q_n+1(x)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{figure}htmlimagethumbnail=0.5,scale=4includegraphicsrewr2sd.epslabelfig:snd{figure}/;
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';
$key = q/{_inline}$displaystyleP_n+1(costheta)=(1+1n)^-12(costheta,P_n(costheta)+2sintheta,Q_n(costheta)pi)(1+O(1n))${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$r_;SPMgt;=max(r,r')${_inline}/;
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';
$key = q/{_inline}$Y_ell^m${_inline}/;
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';
$key = q/{_inline}$r^-ell-1P_ell(cosalpha)${_inline}/;
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';
$key = q/{_inline}$nabla^2U_Q=0${_inline}/;
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';
$key = q/{_inline}$x=cos(theta)${_inline}/;
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';
$key = q/{_inline}$O(1n^alpha)${_inline}/;
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';
$key = q/{_inline}$mathcalI${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$costheta=zr${_inline}/;
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';
$key = q/{_inline}$r'_;SPMgt;=max(r',R)${_inline}/;
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';
$key = q/{_inline}$mathcalZ_ell^m(vecr)=r^-ell-1Y_ell^m(vecrr)${_inline}/;
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';
$key = q/{_inline}$@mathcalK${_inline}/;
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';
$key = q/{_inline}$theta=2${_inline}/;
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$key = q/{displaymath}s_4=displaystylefrac358,c_4,x^4+displaystylefrac52,c_3,x^3+(displaystylefrac32,c_2-displaystylefrac154,c_4),x^2+(c_1-displaystylefrac32,c_3),x+c_0-displaystylefrac12,c_2+displaystylefrac38,c_4>.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatk_nu${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$q_ell${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$vecR${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{figure}htmlimagethumbnail=0.5,scale=4includegraphicsrewr2s.epslabelfig:sn{figure}/;
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';
$key = q/{_inline}$rho_jk(vecr)=phi_j(vecr)phi_k(vecr)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Theta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$A_n(x)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$p_2N(x)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$P_n+1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tau=2${_inline}/;
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';
$key = q/{_inline}$cdot10^2${_inline}/;
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';
$key = q/{_inline}$vecR=2vece_z${_inline}/;
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';
$key = q/{_inline}$theta=45${_inline}/;
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';
$key = q/{_inline}$vece_z${_inline}/;
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$key = q/{_inline}$ell=20${_inline}/;
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';
$key = q/{figure}htmlimagethumbnail=0.5,scale=4includegraphicsrewr2.epslabelfig:gain{figure}/;
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$key = q/{_inline}$cdot10^6${_inline}/;
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';
$key = q/{_inline}$vecRR${_inline}/;
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';
$key = q/{_inline}$gamma_n^(1)=-(2n+5)x${_inline}/;
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';
$key = q/{_inline}$U_Q(vecr)${_inline}/;
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';
$key = q/{_inline}$Q_1(x)=xQ_0(x)-1${_inline}/;
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';
$key = q/{_inline}$sqrtx^2+y^2${_inline}/;
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';
$key = q/{_inline}$Q_n(x)${_inline}/;
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$key = q/{_inline}$q_N(x)${_inline}/;
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$key = q/{_inline}$w_n+1(x)=(2n+1)xw_n(x)(n+1)-nw_n-1(n+1)${_inline}/;
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';
$key = q/{_inline}$P_ell${_inline}/;
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';
$key = q/{_inline}$c_j${_inline}/;
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';
$key = q/{_inline}$nabla^2U=0${_inline}/;
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';
$key = q/{_inline}$vecr${_inline}/;
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';
$key = q/{_inline}$Y_ell^m(theta,phi)${_inline}/;
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';
$key = q/{_inline}$theta${_inline}/;
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$key = q/{_inline}$alpha=310${_inline}/;
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$key = q/{_inline}$tau-${_inline}/;
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';
$key = q/{_inline}$P_1(x)=x${_inline}/;
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';
$key = q/{_inline}$d^(m)${_inline}/;
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$key = q/{_inline}$s_n${_inline}/;
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$key = q/{_inline}$P_n+1(x)${_inline}/;
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$key = q/{_inline}$P_n(x)${_inline}/;
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$key = q/{_inline}$infty${_inline}/;
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$key = q/{_inline}$r=sqrtx^2+y^2+z^2${_inline}/;
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';
$key = q/{_inline}$tau${_inline}/;
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';
$key = q/{_inline}$Sigma${_inline}/;
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$key = q/{_inline}$mathbbR^3${_inline}/;
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';
$key = q/{_inline}$gamma_ell^(0)=ell+2${_inline}/;
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$key = q/{_inline}$^tauomega_n=c_taun${_inline}/;
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$key = q/{_inline}$P_0(x)=1${_inline}/;
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$key = q/{_inline}$omega_n${_inline}/;
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$key = q/{_inline}$vecr'${_inline}/;
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$key = q/{_inline}$delta_n^(k)=1(n+1)${_inline}/;
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$key = q/{_inline}$epsilon${_inline}/;
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';
$key = q/{_inline}$cdot10^3${_inline}/;
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';
$key = q/{_inline}$cdot10^7${_inline}/;
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';
$key = q/{_inline}$r;SPMlt;rho${_inline}/;
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$key = q/{_inline}$r=vertvecrvert${_inline}/;
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$key = q/{_inline}$-lgvert1-s_ellsvert${_inline}/;
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$key = q/{_inline}$Q_n+1(x)${_inline}/;
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$key = q/{_inline}$alpha${_inline}/;
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$key = q/{_inline}$s_n'${_inline}/;
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$key = q/{_inline}$displaystyleP_n(costheta)-mboxifrac2piQ_n(costheta)=exp(mboxintheta)kn^-12left(1+O(1n)right)${_inline}/;
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';
$key = q/{_inline}$rho${_inline}/;
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';
$key = q/{_inline}$s_4'${_inline}/;
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';
$key = q/{_inline}$delta_n^(k)${_inline}/;
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';
$key = q/{_inline}$P_ell+1(costheta)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$gamma;SPMgt;0${_inline}/;
$cached_env_img{$key} = ' 
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$key = q/{_inline}$Q_0(x)=log((1+x)(1-x))2${_inline}/;
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$key = q/{_inline}$K_nu(z)${_inline}/;
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$key = q/{_inline}$vecR_j${_inline}/;
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';
$key = q/{_inline}$omega_n=c_n${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$I[phi_j,phi_k](vecr)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$mathbbR^3tomathbbC${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$mathcalK${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$s_4${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$rRcostheta=vecrcdotvecR${_inline}/;
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';
$key = q/{_inline}$rho(vecr)=exp(-gammar)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$omega_n=omega_n^(0)${_inline}/;
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';
$key = q/{_inline}$omega_n^(k)=1D_n^(k)${_inline}/;
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$key = q/{_inline}$s_ell${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$omega_n^(k)${_inline}/;
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$key = q/{_inline}$s_2N${_inline}/;
$cached_env_img{$key} = ' 
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$key = q/{_inline}$s'_ell${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$nabla^2nmathcalY_ell_1^m_1(nabla)F_ell_2^m_2(r)${_inline}/;
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';
$key = q/{_inline}$gamma_n^(1)=-(2n+5),x_tau${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta=60${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$cdot10^0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$zeta_n^(j)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tau;SPMgt;1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$ell${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$cdot10^4${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$cdot10^8${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$H_2^+${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$rho(vecr)=rho(x,y,z)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$gamma_ell^(1)=-(2ell+5)costheta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$U-U_Q${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$s_2N'=mathcalK_0^(N)({delta_n^(k)},{gamma_n^(j)},{s_n},{omega_n})}${_inline}/;
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';
$key = q/{_inline}$-lgvert1-s'_ellsvert${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$ell=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$phi_j(vecr)${_inline}/;
$cached_env_img{$key} = ' 
';
1;
';
$key = q/{_inline}$rho_jk(vecr)=phi_j(vecr)phi_k(vecr)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$cdot10^6${_inline}/;
$cached_env_img{$key} = '