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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$.

References [Enhancements On Off] (What's this?)

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Keywords: Bessel functions, radial functions
Article copyright: © Copyright 1988 American Mathematical Society

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