# LaTeX2HTML 96.1 (Feb 5, 1996)
# Associate images original text with physical files.

$key = q/{}(j_1,j_2){}/;
$cached_env_img{$key} = ' <IMG WIDTH=34 HEIGHT=15 ALIGN=BOTTOM ALT="tex2html_wrap228" SRC="img15.gif"  > '; 
$key = q/{}(n(m)=sum_jgeqm^inftyN(j)){}/;
$cached_env_img{$key} = ' <IMG WIDTH=142 HEIGHT=23 ALIGN=BOTTOM ALT="tex2html_wrap232" SRC="img19.gif"  > '; 
$key = q/{}(+sqrtj_2(j_2+1)-m_2(m_2pm1);SPMlt;m_1m_2pm1|jm;SPMgt;){}/;
$cached_env_img{$key} = ' <IMG WIDTH=341 HEIGHT=20 ALIGN=BOTTOM ALT="tex2html_wrap244" SRC="img31.gif"  > '; 
$key = q/{}(;SPMlt;j_1j_2m_1m_2|J_z|jm;SPMgt;=){}/;
$cached_env_img{$key} = ' <IMG WIDTH=166 HEIGHT=16 ALIGN=BOTTOM ALT="tex2html_wrap217" SRC="img4.gif"  > '; 
$key = q/{}(N(j)=){}/;
$cached_env_img{$key} = ' <IMG WIDTH=50 HEIGHT=15 ALIGN=BOTTOM ALT="tex2html_wrap230" SRC="img17.gif"  > '; 
$key = q/{}(|m|;SPMgt;j_1+j_2){}/;
$cached_env_img{$key} = ' <IMG WIDTH=90 HEIGHT=16 ALIGN=BOTTOM ALT="tex2html_wrap234" SRC="img21.gif"  > '; 
$key = q/{}(;SPMlt;j_1j_2m_1m_2|jm;SPMgt;=){}/;
$cached_env_img{$key} = ' <IMG WIDTH=144 HEIGHT=16 ALIGN=BOTTOM ALT="tex2html_wrap215" SRC="img2.gif"  > '; 
$key = q/{}(|j_1-j_2|leqjleqj_1+j_2){}/;
$cached_env_img{$key} = ' <IMG WIDTH=154 HEIGHT=16 ALIGN=BOTTOM ALT="tex2html_wrap240" SRC="img27.gif"  > '; 
$key = q/{}(sum_j(2j+1)N(j)=(2j_1+1)(2j_2+1)=sum^j_1+j_2_j=|j_1-j_2|2j+1){}/;
$cached_env_img{$key} = ' <IMG WIDTH=411 HEIGHT=26 ALIGN=BOTTOM ALT="tex2html_wrap241" SRC="img28.gif"  > '; 
$key = q/{}(n(m)=){}/;
$cached_env_img{$key} = ' <IMG WIDTH=53 HEIGHT=15 ALIGN=BOTTOM ALT="tex2html_wrap227" SRC="img14.gif"  > '; 
$key = q/{}(|j_1j_2jm;SPMgt;=sum^j_1_m=-j_1sum^j_2_m_2=-j_2|j_1j_2m_1m_2;SPMgt;;SPMlt;j_1j_2m_1m_2|jm;SPMgt;){}/;
$cached_env_img{$key} = ' <IMG WIDTH=453 HEIGHT=24 ALIGN=BOTTOM ALT="tex2html_wrap225" SRC="img12.gif"  > '; 
$key = q/{}(;SPMlt;j_2j_1m_1m_2|jm;SPMgt;){}/;
$cached_env_img{$key} = ' <IMG WIDTH=131 HEIGHT=16 ALIGN=BOTTOM ALT="tex2html_wrap224" SRC="img11.gif"  > '; 
$key = q/{}(;SPMlt;m_1m_2|j_1j_2j'm';SPMgt;=delta_jj'delta_m'm'){}/;
$cached_env_img{$key} = ' <IMG WIDTH=223 HEIGHT=17 ALIGN=BOTTOM ALT="tex2html_wrap222" SRC="img9.gif"  > '; 
$key = q/{}(;SPMlt;jm|j_1j_2m_1m_2;SPMgt;){}/;
$cached_env_img{$key} = ' <IMG WIDTH=131 HEIGHT=16 ALIGN=BOTTOM ALT="tex2html_wrap216" SRC="img3.gif"  > '; 
$key = q/{}(;SPMlt;j_1j_2m_1m_2|jm;SPMgt;){}/;
$cached_env_img{$key} = ' <IMG WIDTH=131 HEIGHT=16 ALIGN=BOTTOM ALT="tex2html_wrap214" SRC="img1.gif"  > '; 
$key = q/{}(;SPMlt;j_1j_2m_1m_2|jm;SPMgt;=(-1)^j_1+j_2-j){}/;
$cached_env_img{$key} = ' <IMG WIDTH=235 HEIGHT=20 ALIGN=BOTTOM ALT="tex2html_wrap223" SRC="img10.gif"  > '; 
$key = q/{}(;SPMlt;jm|j_1j_2m_1'm_2';SPMgt;=delta_m_1m_1'delta_m_2m_2'){}/;
$cached_env_img{$key} = ' <IMG WIDTH=238 HEIGHT=19 ALIGN=BOTTOM ALT="tex2html_wrap220" SRC="img7.gif"  > '; 
$key = q/{}(J_z=m){}/;
$cached_env_img{$key} = ' <IMG WIDTH=50 HEIGHT=13 ALIGN=BOTTOM ALT="tex2html_wrap229" SRC="img16.gif"  > '; 
$key = q/{}(n(m)=2min(j_2,j_1)+1){}/;
$cached_env_img{$key} = ' <IMG WIDTH=173 HEIGHT=15 ALIGN=BOTTOM ALT="tex2html_wrap237" SRC="img24.gif"  > '; 
$key = q/{}(m=m_1+m_2){}/;
$cached_env_img{$key} = ' <IMG WIDTH=99 HEIGHT=12 ALIGN=BOTTOM ALT="tex2html_wrap226" SRC="img13.gif"  > '; 
$key = q/{}(m_1+m_2=m){}/;
$cached_env_img{$key} = ' <IMG WIDTH=98 HEIGHT=12 ALIGN=BOTTOM ALT="tex2html_wrap218" SRC="img5.gif"  > '; 
$key = q/{}(;SPMlt;j_1j_2m_1m_2|J_1pm+J_2pm|jm;SPMgt;=sqrtj_1(j_1+1)-m_1(m_1mp1);SPMlt;m_1mp1m_2|jm;SPMgt;){}/;
$cached_env_img{$key} = ' <IMG WIDTH=545 HEIGHT=20 ALIGN=BOTTOM ALT="tex2html_wrap243" SRC="img30.gif"  > '; 
$key = q/{}(;SPMlt;j_1j_2m_1m_2|J_pm|jm;SPMgt;=sqrtj(j+1)-m(mpm1);SPMlt;j_1j_2m_1m_2|jmpm1;SPMgt;){}/;
$cached_env_img{$key} = ' <IMG WIDTH=506 HEIGHT=20 ALIGN=BOTTOM ALT="tex2html_wrap242" SRC="img29.gif"  > '; 
$key = q/{}(0leq|m|leq|j_1-j_2|){}/;
$cached_env_img{$key} = ' <IMG WIDTH=131 HEIGHT=16 ALIGN=BOTTOM ALT="tex2html_wrap238" SRC="img25.gif"  > '; 
$key = q/{}(sum_jm;SPMlt;j_1j_2jm|m_1m_2;SPMgt;){}/;
$cached_env_img{$key} = ' <IMG WIDTH=172 HEIGHT=19 ALIGN=BOTTOM ALT="tex2html_wrap221" SRC="img8.gif"  > '; 
$key = q/{}(sum_jm;SPMlt;j_1j_2m_1m_2|jm;SPMgt;){}/;
$cached_env_img{$key} = ' <IMG WIDTH=172 HEIGHT=19 ALIGN=BOTTOM ALT="tex2html_wrap219" SRC="img6.gif"  > '; 
$key = q/{}(n(m)=j_1+j_2+1-|m|){}/;
$cached_env_img{$key} = ' <IMG WIDTH=180 HEIGHT=16 ALIGN=BOTTOM ALT="tex2html_wrap235" SRC="img22.gif"  > '; 
$key = q/{}(N(j)=1){}/;
$cached_env_img{$key} = ' <IMG WIDTH=63 HEIGHT=15 ALIGN=BOTTOM ALT="tex2html_wrap239" SRC="img26.gif"  > '; 
$key = q/{}(J^2=j(j+1)){}/;
$cached_env_img{$key} = ' <IMG WIDTH=93 HEIGHT=17 ALIGN=BOTTOM ALT="tex2html_wrap231" SRC="img18.gif"  > '; 
$key = q/{}(n(m)=0){}/;
$cached_env_img{$key} = ' <IMG WIDTH=65 HEIGHT=15 ALIGN=BOTTOM ALT="tex2html_wrap233" SRC="img20.gif"  > '; 
$key = q/{}(j_1+j_2geq|m|geq|j_1-j_2|){}/;
$cached_env_img{$key} = ' <IMG WIDTH=173 HEIGHT=16 ALIGN=BOTTOM ALT="tex2html_wrap236" SRC="img23.gif"  > '; 

1;