Listar INAMAT2 - Institute for Advanced Materials and Mathematics por autor "2728"
Mostrando ítems 1-12 de 12
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An analytic representation of the second symmetric standard elliptic integral in terms of elementary functions
Bujanda Cirauqui, Blanca ; López García, José Luis ; Pagola Martínez, Pedro Jesús ; Palacios Herrero, Pablo (Springer, 2022) Artículo / ArtikuluaWe 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 ... -
Asymptotic expansions for Moench's integral transform of hydrology
López García, José Luis ; Pagola Martínez, Pedro Jesús ; Pérez Sinusía, Ester (MDPI, 2023) Artículo / ArtikuluaTheis' theory (1935), later improved by Hantush & Jacob (1955) and Moench (1971), is a technique designed to study the water level in aquifers. The key formula in this theory is a certain integral transform H[g](r,t) of ... -
A convergent and asymptotic Laplace method for integrals
López García, José Luis ; Pagola Martínez, Pedro Jesús ; Palacios Herrero, Pablo (Elsevier, 2023) Artículo / ArtikuluaWatson’s lemma and Laplace’s method provide asymptotic expansions of Laplace integrals F (z) := ∫ ∞ 0 e −zf (t) g(t)dt for large values of the parameter z. They are useful tools in the asymptotic approximation of ... -
Convergent expansions of the Bessel functions in terms of elementary functions
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 confluent hypergeometric functions in terms of elementary functions
Bujanda Cirauqui, Blanca ; López García, José Luis ; Pagola Martínez, Pedro Jesús (American Mathematical Society, 2018) Artículo / ArtikuluaWe consider the confluent hypergeometric function M(a, b; z) for z ∈ C and Rb >Ra > 0, and the confluent hypergeometric function U(a, b; z) for b ∈ C, Ra > 0, and Rz > 0. We derive two convergent expansions of M(a, b; z); ... -
Convergent expansions of the incomplete gamma functions in terms of elementary functions
Bujanda Cirauqui, Blanca ; López García, José Luis ; Pagola Martínez, Pedro Jesús (World Scientific Publishing, 2017) Artículo / ArtikuluaWe 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 ... -
New analytic representations of the hypergeometric functions p+1Fp
López García, José Luis ; Palacios Herrero, Pablo ; Pagola Martínez, Pedro Jesús (Springer, 2021) Artículo / ArtikuluaThe power series expansions of the hypergeometric functions p+1Fp (a,b1,…,bp;c1,…,cp;z) converge either inside the unit disk |z|<1 or outside this disk |z|>1. Nørlund’s expansion in powers of z/(z−1) converges in the ... -
The Pearcey integral in the highly oscillatory region
We consider the Pearcey integral P(x, y) for large values of |y| and bounded values of |x|. The integrand of the Pearcey integral oscillates wildly in this region and the asymptotic saddle point analysis is complicated. ... -
Series representations of the Volterra function and the Fransén–Robinson constant
López García, José Luis ; Pagola Martínez, Pedro Jesús ; Palacios Herrero, Pablo (Elsevier, 2021) Artículo / ArtikuluaThe Volterra function μ(t,β,α) was introduced by Vito Volterra in 1916 as the solution to certain integral equations with a logarithmic kernel. Despite the large number of applications of the Volterra function, the only ... -
Uniform approximations of the first symmetric elliptic integral in terms of elementary functions
Bujanda Cirauqui, Blanca ; López García, José Luis ; Pagola Martínez, Pedro Jesús ; Palacios Herrero, Pablo (Springer, 2022) Artículo / ArtikuluaWe 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 ... -
Uniform convergent expansions of integral transforms
López García, José Luis ; Palacios Herrero, Pablo ; Pagola Martínez, Pedro Jesús (American Mathematical Society, 2021) Artículo / ArtikuluaSeveral 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 ... -
Uniformly convergent expansions for the generalized hypergeometric functions p –1Fp and pFp
López García, José Luis ; Pagola Martínez, Pedro Jesús ; Karp, D. B. (Taylor & Francis, 2020) Artículo / ArtikuluaWe 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 ...