% GCHRI1 Alternative modification by a linear divisor.
%
% Given a weight function w(t) through the first numax recurrence
% coefficients ab0 of its orthogonal polynomials, [ab,rho,nu]=
% GCHRI1(n,ab0,x,eps0,nu0,numax) uses the modified Chebyshev
% algorithm to generate to a relative accuracy eps0 the first n
% recurrence coefficients of the orthogonal polynomials
% relative to the modified weight function w(t)/(t-x). The
% required modified moments are generated by a continued
% fraction algorithm, which involves backward recursion from
% nu down to 0. The starting index nu is increased by 5 until
% convergence of the continued fraction algorithm is obtained.
% The initial value of nu to be used is nu0, and nu is not
% allowed to exceed numax. The output variable nu is either
% numax, if there is no convergence, or the final value of
% nu achieving convergence. The alpha- and beta-coefficients
% of the given weight function are to be provided in the first
% and second column of the numax x 2 input array ab0; those
% of the modified weight function are returned in the first and
% second column of the nx2 output array ab. The Cauchy
% integrals, which except for the sign are the modified
% moments, are stored in the output array rho.
%
function [ab,rho,nu]=gchri1(N,ab0,x,eps0,nu0,numax)
if N<1, error('N out of range'), end
N0=size(ab0,1); if N0