𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Taylor expansions for distributions

✍ Scribed by R. Estrada; R. P. Kanwal

Publisher
John Wiley and Sons
Year
1993
Tongue
English
Weight
319 KB
Volume
16
Category
Article
ISSN
0170-4214

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

We present the Taylor asymptotic expansion of a perturbed distribution of the form
equation image
is a smooth function defined in ℝ^n^. First we present the one‐dimensional theory to illustrate the underlying concepts and then we discuss the multi‐dimensional case. We find that various known results follow as special limits of our results.

πŸ“œ SIMILAR VOLUMES

Taylor Expansion for Generalized Functio
Taylor Expansion for Generalized Functions
✍ B. StankoviΔ‡ πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 131 KB

A necessary and sufficient condition is given that the asymptotic Taylor expan-Ε½ . sion for a distribution for an ultradistribution is the Taylor series convergent in Ε½ . the space of distributions of ultradistributions .

Addition theorems as three-dimensional T
Addition theorems as three-dimensional Taylor expansions
✍ Ernst Joachim Weniger πŸ“‚ Article πŸ“… 2000 πŸ› John Wiley and Sons 🌐 English βš– 351 KB

A principal tool for the construction of the addition theorem of a r Јиّ ## Ž . function f is the translation operator e , which generates f r q rЈ by doing a threedimensional Taylor expansion of f around r. In atomic and molecular quantum mechanics, one is usually interested in irreducible spheri

Asymptotic Expansions for Large Deviatio
Asymptotic Expansions for Large Deviation Probabilities of Noncentral Generalized Chi-Square Distributions
✍ W.-D Richter; J Schumacher πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 265 KB

Asymptotic expansions for large deviation probabilities are used to approximate the cumulative distribution functions of noncentral generalized chi-square distributions, preferably in the far tails. The basic idea of how to deal with the tail probabilities consists in first rewriting these probabili

A Taylor expansion algorithm for integra
A Taylor expansion algorithm for integration of 3D near-hypersingular integrals
✍ Mi, Y. ;Aliabadi, M. H. πŸ“‚ Article πŸ“… 1996 πŸ› John Wiley and Sons 🌐 English βš– 626 KB

An algorithm based on the Taylor series expansion is extended to deal with the problem of nearhypersingular integrals occurring in a 3D electrostatic BEM formulation. The integral is evaluated by subtracting out the leading terms in the near-hypersingular part of the integrand and adding it back. Th