\\ PARI/GP code for computing 275 digits of the result of Problem 3 \\ Working precision dec=279, 15 days computation time (1.6 GHz processor) \\ Transformation (3.30), truncation point T: (3.31), step size 1/r: (3.32) \\ Power iteration enhanced by Wynn's epsilon algorithm, maxiter = 27 \\ Save as PROBLEM3, run (in the background) with "nice +19 gpout&" \\ View the current state of the output file with "more out" {inprod(x,y) = sum(j=1,N1,real(x[j])*real(y[j])-imag(x[j])*imag(y[j]))} {dig(eps) = if(eps==0,dec,-log(abs(eps))/log(10))} {Wynn(vals,L) = L2=2*L-1; vv=vector(L2,j, if(j%2==1, vals[(j+1)/2], 0)); for(j=2,L, forstep(k=j, L2+1-j, 2, vv[k]=vv[k]+1/(vv[k+1]-vv[k-1]))); vector(L,j, vv[2*j-1])} {problem3(T,r,tol,maxiter) = \\ T=truncation limit, r=1/step, tol=error tolerance h=1/r; N=floor(T*r); N1=N+1; s=vector(N1,k,h*(k-N1)); y=vector(N1); t=vector(N1,k,s[k]+s[k]^3/3); dt=vector(N1,k,h*(1+s[k]^2)); \\t=Phi1(s) z=vector(N1,k,sqrt(1/2)*(cosh(t[k])-I*sinh(t[k]))); zbar=conj(z); \\contour z1=vector(N1,k, z[k]-1/2); z2=vector(N1,k, -2*z[k]+7/4); \\auxiliary vectors ct=vector(N1,k,if(abs(imag(z[k]))<925412,cotan(Pi*z[k]),sign(imag(z[k]))/I)); w=vector(N1,k, -ct[k]*zbar[k]*dt[k]); w[N1]=w[N1]/2; x0=vector(N1,j, 2/(z[j]^2+z[j]))~; x=x0/x0[N1]; wbest=0; wbest0=1; iter=0; while ( abs(wbest-wbest0)>tol & iter