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

As to the Bessel integrals of type \displaystyle \int _0^x \left (x^\mu -t^\mu \right )^\lambda t^\alpha J_\beta (t)dt\qquad (x>0), 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 ext...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society. Series B 2018-05, Vol.5 (4), p.25-39
Main Authors: Cho, Yong-Kum, Chung, Seok-Young, Yun, Hera
Format: Article
Language:English
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Summary:As to the Bessel integrals of type \displaystyle \int _0^x \left (x^\mu -t^\mu \right )^\lambda t^\alpha J_\beta (t)dt\qquad (x>0), 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.
ISSN:2330-1511
2330-1511
DOI:10.1090/bproc/34