TY - JOUR
T1 - Application of the Hadamard's finite part concept to the asymptotic expansion of a class of multidimensional integrals
AU - Sellier, A.
PY - 1996/5/15
Y1 - 1996/5/15
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.
U2 - 10.1098/rsta.1996.0045
DO - 10.1098/rsta.1996.0045
M3 - Article
AN - SCOPUS:3142631834
SN - 1364-503X
VL - 354
SP - 1195
EP - 1246
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
IS - 1710
ER -