A computational method for hypersurfaces in terms of gamma function
type: Item
instance of: scholarly article
title: A computational method for hypersurfaces in terms of gamma function
zbMATH Open document ID: 1069.65021
published in: Applied Mathematics and Computation
publication date: 2005-02-22T00:00:00Z
review text: The author provides a general volume formula for regions often considered in physical and engineering problems. Dirichlet integrals in terms of beta and gamma functions can be obtained by performing a suitable variable transformation from Cartesian to polar coordinates and vice versa. The main idea is to extend the computation of such integrals having 2D integration domain to find volumes of a wide range of \(n\)-dimensional axially symmetric regions given by the equation \[ G(x)=\sum_{i=1}^n\biggl|{{x_i}\over{a_i}}\biggr|^{\alpha_i}-1=0, \] \(x_i\) real, \(\alpha_i\) and \(a_i,\;i=1,\ldots,n\) positive constants. First volume of regions bounded by hypersurfaces are considered. Then a generalization to more elaborate shapes is presented. Finally an algorithm for the numerical computation of such volumes is proposed, where an asymptotic expansion of the gamma function is given by Stirling's formula.
reviewed by: Paola Lamberti
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 41A55
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 2136878
zbMATH Keywords: beta function
zbMATH Keywords: gamma function
zbMATH Keywords: hypersurfaces
zbMATH Keywords: Dirichlet function
zbMATH Keywords: Stirling's formula
zbMATH Keywords: volume formula
zbMATH Keywords: algorithm
author: Nuri Ozalp
MaRDI profile type: Publication
full work available at URL: j.amc.2003.12.070
OpenAlex ID: W2026670851
cites work: Q4515161
cites work: Q4940095
cites work: A general solution of the diffusion equation for semiinfinite geometries
DOI: 10.1016/J.AMC.2003.12.070
description: scientific article; zbMATH DE number 2136878