A convergent version of Watson’s lemma for double integrals
Fecha
2022Versión
Acceso abierto / Sarbide irekia
Tipo
Artículo / Artikulua
Versión
Versión publicada / Argitaratu den bertsioa
Impacto
|
10.1080/10652469.2022.2098955
Resumen
A modification of Watson’s lemma for Laplace transforms ∞
0 f(t)
e−zt dt was introduced in [Nielsen, 1906], deriving a new asymptotic
expansion for large |z| with the extra property of being convergent as well. Inspired in that idea, in this paper we derive asymptotic expansions of two-dimensional Laplace transforms F(x, y) := ∞
0
∞
0 f(t,s) e−xt−ys dt ds for large |x| and |y| that are al ...
[++]
A modification of Watson’s lemma for Laplace transforms ∞
0 f(t)
e−zt dt was introduced in [Nielsen, 1906], deriving a new asymptotic
expansion for large |z| with the extra property of being convergent as well. Inspired in that idea, in this paper we derive asymptotic expansions of two-dimensional Laplace transforms F(x, y) := ∞
0
∞
0 f(t,s) e−xt−ys dt ds for large |x| and |y| that are also convergent. The expansions of F(x, y) are accompanied by error bounds.
Asymptotic and convergent expansions of some specialfunctions are
given as illustration. [--]
Materias
Asymptotic expansions of integrals,
Watson’s lemma for double integrals,
Double Laplace transform,
Convergent expansions,
Special functions
Editor
Taylor & Francis
Publicado en
Integral Transforms and Special Functions (2022)
Departamento
Universidad Pública de Navarra. Departamento de Estadística, Informática y Matemáticas /
Nafarroako Unibertsitate Publikoa. Estatistika, Informatika eta Matematika Saila /
Universidad Pública de Navarra/Nafarroako Unibertsitate Publikoa. Institute for Advanced Materials and Mathematics - INAMAT2
Versión del editor
Entidades Financiadoras
Open access funding provided by Universidad Pública de Navarra
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