An extension of positivity for integrals of Bessel functions and Buhmann's radial basis functions

Abstract

As to the Bessel integrals of type \begin{equation*} \int_0^x \left(x^μ-t^μ\right)^λt^αJ_β(t)dt\qquad(x>0), \end{equation*} we improve known positivity results by making use of new positivity criteria for ${}_1{F}_2$ and ${}_2{F}_3$ generalized hypergeometric functions. As an application, we extend Buhmann's class of compactly supported radial basis functions.

15 pages, 4 figures