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An analytic representation of the second symmetric standard elliptic integral in terms of elementary functions
(Springer, 2022)
Artículo / Artikulua,
We derive new convergent expansions of the symmetric standard elliptic integral RD(x,y,z), for x,y,z∈C∖(−∞,0], in terms of elementary functions. The expansions hold uniformly for large and small values of one of the three ...
Uniform convergent expansions of integral transforms
(American Mathematical Society, 2021)
info:eu-repo/semantics/article,
Several convergent expansions are available for most of the special functions of the mathematical physics, as well as some asymptotic expansions [NIST Handbook of Mathematical Functions, 2010]. Usually, both type of ...
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 ...
Uniform approximations of the first symmetric elliptic integral in terms of elementary functions
(Springer, 2022)
info:eu-repo/semantics/article,
We consider the standard symmetric elliptic integral RF(x, y, z) for complex x, y, z. We derive convergent expansions of RF(x, y, z) in terms of elementary functions that hold uniformly for one of the three variables x, y ...
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 ...