On the generalized Stieltjes transform of distributions
type: Item
instance of: scholarly article
title: On the generalized Stieltjes transform of distributions
zbMATH Open document ID: 0605.46034
author: B. George
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1986-01-01T00:00:00Z
review text: We obtain the generalized Stieltjes transform: \[ F(x)=\frac{\Gamma (A)}{\Gamma (B)}\frac{\Gamma (\beta +1)}{x}\int^{\infty}_{0}(\frac{t}{x})^{\beta}_ 2F_ 1(A,\beta +1;B;-\frac{t}{x})f(t)dt \] where \(A=\beta +\eta +1\), \(B=\alpha +A\), \(\beta\geq 0\) and \(\eta >0\), by the iteration of the generalized Laplace transform, in distributional sense. We discuss the above transform as a special case of convolution transform (in distributional sense) and prove an inversion formula for the above transform in distributional sense.
Mathematics Subject Classification ID: 46F12
Mathematics Subject Classification ID: 44A15
zbMATH DE Number: 3977699
zbMATH Keywords: generalized Stieltjes transform
zbMATH Keywords: iteration of the generalized Laplace transform
zbMATH Keywords: convolution transform
zbMATH Keywords: inversion formula
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3977699