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As to the Bessel integrals of type \begin{equation*} \int_0^x\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 newpositivity criteria for ${}_1F_2$ and ${}_2F_3$ generalized hypergeometricfunctions. As an application, we extend Buhmann's class of compactly supportedradial basis functions.

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