Now showing items 1-7 of 7

• #### Convergent asymptotic expansions of Charlier, Laguerre and Jacobi polynomials ﻿

(Cambridge University Press, 2004) ﻿ ﻿ Artículo / Artikulua
Convergent expansions are derived for three types of orthogonal polynomials: Charlier, Laguerre and Jacobi. The expansions have asymptotic properties for large values of the degree. The expansions are given in terms of ...
• #### Convergent expansions of the Bessel functions in terms of elementary functions ﻿

(Springer US, 2018) ﻿ ﻿ Artículo / Artikulua
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) ﻿ ﻿ Artículo / Artikulua
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 convergent expansions of integral transforms ﻿

(American Mathematical Society, 2021) ﻿ ﻿ Artículo / Artikulua
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 ...
• #### Uniform convergent expansions of the Gauss hypergeometric function in terms of elementary functions ﻿

(Taylor & Francis, 2018) ﻿ ﻿ Artículo / Artikulua
We consider the hypergeometric function 2F1(a, b; c; z) for z ∈ C \ [1,∞). For Ra ≥ 0, we derive a convergent expansion of 2F1(a, b; c; z) in terms of the function (1 − z)−a and of rational functions of z that is uniformly ...
• #### Uniform representation of the incomplete beta function in terms of elementary functions ﻿

(Kent State UniversityJohann Radon Institute (RICAM), 2018) ﻿ ﻿ Artículo / Artikulua
We consider the incomplete beta function Bz(a, b) in the maximum domain of analyticity of its three variables: a, b, z ∈ C, −a /∈ N, z /∈ [1, ∞). For <b ≤ 1 we derive a convergent expansion of z−aBz(a, b) in terms of the ...
• #### Uniformly convergent expansions for the generalized hypergeometric functions p –1Fp and pFp ﻿

(Taylor & Francis, 2020) ﻿ ﻿ Artículo / Artikulua
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 ...