% SR_LAGUERRELOG0 This computes the first N recurrence % coefficients alpha_k, beta_k, k=0,1,\ldots,N-1, to an % accuracy of nofdig digits for the system of polynomials % orthogonal with respect to the weight function % w(x)=x^a e^{-x}(x-1-log x), % using ordinary moments. The output variable ab is the % Nx2 array of the nofdig-digit recurrence coefficients, % and dig is the number of digits required to achieve the % target precision of nofdig decimal places using successive % calculations with precisions incremented in steps of dd % digits. The number dd in the first statement of the % routine, as well as dig0, can be changed by the user as % seen appropriate. % function [ab,dig]=sr_laguerrelog0(N,a,nofdig) syms mom ab ab0 ab1 abn dd=10; dig0=nofdig; ii=dig0-dd; maxerr=1; while maxerr>.5*10^(-nofdig) ii=ii+dd; dig=ii mom=momlaglog(dig,N,a); if ii==dig0 ab0=schebyshev(dig,N,mom); else ab1=schebyshev(dig,N,mom); serr=vpa(abs((ab1-ab0)./ab1),dig); err=subs(serr); maxerr=max(max(err)); ab0=ab1; end end ab=vpa(ab1,nofdig);