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Convergent expansions of the Bessel functions in terms of elementary functions
(Springer US, 2018) info:eu-repo/semantics/article,
We consider the Bessel functions Jν (z) and Yν (z) for ν > −1/2 and z ≥ 0. We derive a convergent expansion of Jν (z) in terms of the derivatives of (sin z)/z, and a convergent expansion of Yν (z) in terms of derivatives ...
Convergent expansions of the incomplete gamma functions in terms of elementary functions
(World Scientific Publishing, 2017) info:eu-repo/semantics/article,
We consider the incomplete gamma function γ(a,z) for Ra>0 and z∈C. We derive several convergent expansions of z−aγ(a,z) in terms of exponentials and rational functions of z that hold uniformly in z with Rz bounded from ...
Uniformly convergent expansions for the generalized hypergeometric functions p –1Fp and pFp
(Taylor & Francis, 2020) info:eu-repo/semantics/article,
We derive a convergent expansion of the generalized hypergeometric function p−1 F p in terms of the Bessel functions 0 F 1 that holds uniformly with respect to the argument in any horizontal strip of the complex plane. We ...