Work

Integration of Monomials over the Unit Sphere and Unit Ball in Rn

Year: 2025

Type: article

Abstract: We compute the integral of monomials of the form x2β over the unit sphere and the unit ball in Rn where β = (β1, . . . , βn) is a multi–index with real components βk > −1/2, 1 ≤ k ≤ n, and discuss their asymptotic behavior as some, or all, βk → ∞. This allows for the evaluation of integrals involving circular and hyperbolic trigonometric functions over the unit sphere and the unit ball in Rn. We also consider the Fourier transform of monomials xα restricted to the unit sphere in Rn, where the multi–indices α have integer components, and discuss their behaviour at the origin.

Source: Selecciones Matemáticas

DOI: 10.17268/sel.mat.2025.01.01

Authors: Calixto P. Calderón, Alberto Torchinsky

Institutions: University of Illinois Chicago, Indiana University Bloomington, Indiana University

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4412771791

FWCI: 1.886

Cites:

Cited by: 1

Related to: 10