Note on backward recurrence algorithms

Abstract

An algorithm is given for the computation of the recessive solution of a secondorder linear difference equation, based upon a combination of algorithms due to J.C.P. Miller and F.W.J. Olver. A special feature is automatic and rigorous control of truncation error. The method is illustrated by application to the well-used example of the Bessel functions J r ( x ) {J_r}(x) .