An investigation of uniform expansions of large order Bessel functions in Gravitational Wave Signals from Pulsars

Abstract

In this work, we extend the analytic treatment of Bessel functions of large order and/or argument. We examine uniform asymptotic Bessel function expansions and show their accuracy and range of validity. Such situations arise in a variety of applications, in particular the Fourier transform of the gravitational wave signal from a pulsar. The uniform expansion we consider here is found to be valid in the entire range of the argument.