Continued fraction evaluation of Jn (x)/Jn-1 (x)

A.S. AL-FHAID

epartment of Mathematics , College of Sciences, P.O.Box 80203, King Abdulaziz University, Jeddah-21589 (Saudi Arabia).

Received on March 26, 2010 and accepted on April 26, 2010

ABSTRACT

In this paper, continued fraction expansion for the Bessel funcions ratio Jn (x)/Jn-1 (x) was developed. An efficient and simple computational algorithm based on this expansion was also developed using top-down evaluation procedure.Numerical results of the algorithm are in full agreement at least to fifteen digits accuracy with that of the standared tables.

Keywords : Bessel functions , continued fraction ,special functions, number theroy.