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An extension of positivity for integrals of Bessel functions and Buhmann's radial basis functions (1805.11863v1)
Published 30 May 2018 in math.CA
Abstract: As to the Bessel integrals of type \begin{equation*} \int_0x \left(x\mu-t\mu\right)\lambda t\alpha J_\beta(t)dt\qquad(x>0), \end{equation*} we improve known positivity results by making use of new positivity criteria for ${}_1F_2$ and ${}_2F_3$ generalized hypergeometric functions. As an application, we extend Buhmann's class of compactly supported radial basis functions.