% USPCONJ Conjecture for the smallest zero of ultraspherical polynomials % function lam0=uspconj(n,dl) eps0=1e2*eps; lam=1; k0=0; while k0==0 lam=lam+dl; k0=uspineq(n,lam); end lr=lam; ll=lam-dl; while lr-ll>eps0 lam0=.5*(ll+lr); k0=uspineq(n,lam0); if k0>0 lr=lam0; else ll=lam0; end end