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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A new proof of Sonine's formula


Author: Krzysztof Stempak
Journal: Proc. Amer. Math. Soc. 104 (1988), 453-457
MSC: Primary 33A40
MathSciNet review: 962812
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Abstract: We give a new proof of an old integral formula due to Sonine in which the Bessel functions are involved. By considering the Banach algebra of radial functions on $ {{\mathbf{R}}^n},n \geq 2$, we observe that Sonine's formula is valid for all positive integers. Next, a complex function theory argument is applied to obtain the validity of the formula for all complex parameters $ z$ with Re $ z > 0$.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0962812-X
Keywords: Bessel functions, radial functions
Article copyright: © Copyright 1988 American Mathematical Society