Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Hyperasymptotic evaluation of the Pearcey integral via Hadamard expansions
Journal of Computational and Applied Mathematics - Special issue: International conference on mathematics and its application
On the use of Hadamard expansions in hyperasymptotic evaluation of Laplace-type integrals-IV: Poles
Journal of Computational and Applied Mathematics
Effective Laguerre Asymptotics
SIAM Journal on Numerical Analysis
| Hi-index | 7.29 |
We present a method of high-precision calculation of the Bessel functions using Hadamard series. Such series are absolutely convergent expansions involving the normalised incomplete gamma function P(a,z)=@c(a,z)/@C(a) and possess early terms that behave like those in an asymptotic expansion. In the case of real variables the function P(a,z) acts as a smoothing factor on the terms of the series. We show how these series representing the Bessel functions of complex argument can be chosen so as to produce rapidly convergent series that possess terms decaying at the geometric rate @q^k, where 0