Application of the Hadamard's finite part concept to the asymptotic expansion of a class of multidimensional integrals

A. Sellier

doi:10.1098/rsta.1996.0045

Application of the Hadamard's finite part concept to the asymptotic expansion of a class of multidimensional integrals

A. Sellier

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

The aim of this paper is to study the expansion with respect to the large and real parameter A of the integral (Equation Presented) where for i ∈ {1, . . . ,n} : ai > 0, l_i ∈ ℕ and α_i is complex with Re(α_i) > -1. Moreover, f is a smooth enough function and g belongs to B_r(]0, +∞[), a space defined below. The derivation of such an asymptotic expansion is established by induction on the integer n and makes use of a basic concept: the integration in the finite part sense of Hadamard.

langue originale	Anglais
Pages (de - à)	1195-1246
Nombre de pages	52
journal	Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	354
Numéro de publication	1710
Les DOIs	https://doi.org/10.1098/rsta.1996.0045
état	Publié - 15 mai 1996

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10.1098/rsta.1996.0045

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abstract = "The aim of this paper is to study the expansion with respect to the large and real parameter A of the integral (Equation Presented) where for i ∈ \{1, . . . ,n\} : ai > 0, li ∈ ℕ and αi is complex with Re(αi) > -1. Moreover, f is a smooth enough function and g belongs to Br(]0, +∞[), a space defined below. The derivation of such an asymptotic expansion is established by induction on the integer n and makes use of a basic concept: the integration in the finite part sense of Hadamard.",

author = "A. Sellier",

year = "1996",

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day = "15",

doi = "10.1098/rsta.1996.0045",

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Application of the Hadamard's finite part concept to the asymptotic expansion of a class of multidimensional integrals. / Sellier, A.
Dans: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol 354, Numéro 1710, 15.05.1996, p. 1195-1246.

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

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N2 - The aim of this paper is to study the expansion with respect to the large and real parameter A of the integral (Equation Presented) where for i ∈ {1, . . . ,n} : ai > 0, li ∈ ℕ and αi is complex with Re(αi) > -1. Moreover, f is a smooth enough function and g belongs to Br(]0, +∞[), a space defined below. The derivation of such an asymptotic expansion is established by induction on the integer n and makes use of a basic concept: the integration in the finite part sense of Hadamard.

AB - The aim of this paper is to study the expansion with respect to the large and real parameter A of the integral (Equation Presented) where for i ∈ {1, . . . ,n} : ai > 0, li ∈ ℕ and αi is complex with Re(αi) > -1. Moreover, f is a smooth enough function and g belongs to Br(]0, +∞[), a space defined below. The derivation of such an asymptotic expansion is established by induction on the integer n and makes use of a basic concept: the integration in the finite part sense of Hadamard.

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DO - 10.1098/rsta.1996.0045

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SN - 1364-503X

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JO - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

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ER -

Application of the Hadamard's finite part concept to the asymptotic expansion of a class of multidimensional integrals

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