On a class of orthogonal polynomials (Q1173990)

The authors prove the following Theorem: Let \(P_ n\), \(n=0,1,\dots,\) be orthogonal polynomials on \((-1,1)\) with weight \(\rho\), \(\deg P_ n=n\), \(P_ n(1)=1\) and let \(P_ n\) fulfill the recurrence relation \[ P_ n(x)=(A_ n x+B_ n)P_{n-1}(x)-C_ n P_{n-2}(x),\qquad n=2,3,\dots, \] then for the polynomials \(\tilde P_ n\) orthogonal on \((- 1,1)\) with weight \((1-x)\rho(x)\) the same recurrence relation is valid with coefficients \(\tilde A_ n\), \(\tilde B_ n\), \(\tilde C_ n\) given by \[ \tilde A_ n=A_{n+1}, \qquad \tilde B_ n=B_{n+1}+(A_{n+1}- A_ n)/A_ n, \qquad \tilde C_ n=C_ n A_{n+1}/A_ n. \] An example is added.