# LaTeX2HTML 95 (Thu Jan 19 1995)
# Associate image original text (scrambled) with physical files.
$key = q/{displaymath}W_N(k^2_N,1-k^2_N)=0.{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$x_N${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$lambda${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$k_1:=k(q^p)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$log_23=1.58cdots;SPM_lt;2${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$3sqrt7${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$q=e^-pisqrtr${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$x:=(x_0,x_1,x_2,cdots,x_n-1)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}s_n+1:=frac25(z+xz+1)^2s_n,{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$lambda(t)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}C(x,y)=F^-1[F(x)F(y)].{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}z:=left[frac12xleft(y+sqrty^2-4x^3right)right]^15.{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$k_i+1${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}arctanx=int^x_0fracdt1+t^2=x-fracx^33+fracx^55-cdotsquad|x|leq1{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$pi${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}3^10_71;SPM_lt;pi;SPM_lt;3^1_7.{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}F[C(x,y)]=F(x)F(y){displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$O(n(logn)(loglogn))${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$o(n)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$p(p+1)(p-1)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$10^n${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$Kpi${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}fracTheta_2(q^p)Theta_3(q^p)=v^2quadmboxandquadfracTheta_2(q)Theta_3(q)=u^2{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$lambda_5${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$W_5${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$2^27${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$O(nM(n))${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$O(M(n))${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$K(k)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$k(q)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$b_0:=3${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}eta(q):=q^frac112prod^infty_n=1(1-q^2n).{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$O(n^2)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$C(x,y)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$W_58${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$times${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$e^pi${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$rrightarrowp^2r${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$lambda_i${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$y:=(y_0,y_1,y_2,cdots,y_n-1)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$d_n(N)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}k:=k(q)quadmboxandquadq:=e^-pisqrtr.{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$p:=2,3,4,5,${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}frac1pi=fracsqrt89801sum^infty_n=0frac(4n)!(n!)^4frac[1103+26390n]396^4n.{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$k_0:=k(q)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$O((logn)M(n))${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$pi+log2+sqrt2log3${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}${mboximenskipt;SPM_gt;0}${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$2^n${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$p:=4${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$e^-2piiN${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}fracpi4=4arctanleft(frac15right)-arctanleft(frac1239right).{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$318${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$2^k${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$lambda_p${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$exp(lambda^-1(g(z)))${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$6cdot2^n${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}lambda_i:=lambda(z^iq^1p)quadi;SPM_lt;p{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}y_n+1:=frac1-(1-y^4_n)^141+(1-y^4_n)^14{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}0;SPM_lt;leftvertbeta-fracpqrightvert;SPM_lt;frac1q^n.{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$g_58${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$Theta_2${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$O(M(n)logn)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$sqrty${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$a_0:=2sqrt3${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$p:=5${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}q:=e^ipit,quadmboxthenquadtaurightarrowtau+2quadmboxandquadtaurightarrowfractau(2tau+1){displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$b_n${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$2+epsilon${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$2^60${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}frac1pi=sum^infty_n=0left(arrayc2nnarrayright)^3frac42n+52^12n+4.{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$exp${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$dKdk${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}z_k=C_k(x,y)=sum^N-1_j=0x_jy_k-j,{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}q:=e^ipit.{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$Gamma${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}x_k+1=2x_k-x^2_ky{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}k^prime:=sqrt1-k^2{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$pi+e${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$1y${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$infty${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$z:=(z_0,z_1,z_2,cdots,z_n-1)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$16cdot2^12n${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}w(t):=fracat+bct+d,{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}x:=frac5Theta_3(q^5)Theta_3(q)-1quadandquady:=(x-1)^2+7.{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$_3F_2${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$bfQ(v)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$beta${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}O(n^log_23).{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$E(k)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$v:=lambda^18${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}K^prime(k):=K(k^prime)quadmboxandquadE^prime(k):=E(k^prime).{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$logpi${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$k_i${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$dot${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$M_p:=M_p(k_0,k_1)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$10^9${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$(0,-1),(0,0),(i,infty)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$5m2^m${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$N:=58${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}x_N:=frac4k_N(k^prime_N)^2(1+k^2_N)^2:=left(fracg^12_N+g_N^-122right)^1.{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$qrightarrowq^p${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$pgeq5${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$F_G${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$a_n${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$bfQ(lambda)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}f(g(z))=f(z)quadforallginG.{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$1pi${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$sqrt2${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$lambda^18,:Omega_5${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}Theta_3(t,q):=sum^infty_n=-inftyq^n^2e^piintenskipquad(mboximenskipt;SPM_gt;0){displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$(t=0)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}k_N:=k(e^-pisqrtN),quadg^12_N=(k^prime_N)^2(2k_N).{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$F^-1(x)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$14^n${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}lambda(w(t)):=lambda(t){displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}x_k+1=fracx_k(3-yx^2_k)2{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$_2F_1${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}frac2K(k_0)pi=M^-1_p(k_0,k_1)M_p^-1(k_1,k_2)M_p^-1(k_2,k_3)cdots.{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$zeta(3)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$lambda^-1${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$gamma${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$W_p${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$k(q^p)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$1sqrty${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$O(logn)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$e^pi=(-1)^-i${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}frac4k(k^prime)^2(1+k^2)^2=left(fracg^12+g^-122right)^-1{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$u:=x^18${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$2^6n${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}k_1=frac2sqrtk1+k.{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$k_i:=k(q^p^i)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$k_N${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}x:=5s_n-1quady:=(x-1)^2+7{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$0;SPM_lt;k;SPM_lt;1)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$pie${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$x_k${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$c^overlinen${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$A_5${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}frac1pi=fracsqrt89801sum^infty_n=0frac(4n)!(n!)^4frac[1103+26390n]396^4n{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$K^prime${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$M_p${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$s_n${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$epsilon;SPM_gt;0${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$y_0:=sqrt2-1${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$E^prime${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}27090964785531389931563200281035226311929052227303times2^923^195^2011^253.{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$lambda_0${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$c^overlinen:=c(c+1)(c+2)cdots(c+n-1).${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}g^2_58=left(fracsqrt29+52right){displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$O((logn)^2+epsilonn)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$N=2^m${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$O(n)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$Omega_5${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$K(k_1)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$(N=58)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$(p=11)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$O(c^p^i)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$0.10100100001cdots${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}lambda_p:=lambda(q^p).{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$s_0:=5(sqrt5-2)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}w(t)=fracat+bct+d,{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$O((logn)^2M(n))${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}x_k+1=frac12left(x_k+fracyx_kright){displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$O(m(n))${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$bfQ(lambda,lambda_0)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$F(x)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$2^2m+3${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$s:=1M_5(k_0,k_1)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$31381${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$M(n)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$p(p-1)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}r_i:=frac12xleft(ypmsqrty^2-4x^3right){displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}a_n+1:=frac2a_nb_na_n+b_nquadmboxandquadb_n+1:=sqrta_n+1b_n.{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$k_0${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}(a+b10^n)(c+d10^n)=ac-[(a-b)(c-d)-ac-bd]10^n+bd10^2n,{displaymath}/;
$cached_env_img{$key} ='
';
1;