A new proof of Sonine’s formula
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- by Krzysztof Stempak PDF
- Proc. Amer. Math. Soc. 104 (1988), 453-457 Request permission
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
- Billie Chandler Carlson, Special functions of applied mathematics, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1977. MR 0590943
- Douglas L. Guy, Hankel multiplier transformations and weighted $p$-norms, Trans. Amer. Math. Soc. 95 (1960), 137–189. MR 120506, DOI 10.1090/S0002-9947-1960-0120506-1 E. C. Titchmarsh, The theory of functions, Oxford Univ. Press, London, 1939.
- G. N. Watson, A treatise on the theory of Bessel functions, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1995. Reprint of the second (1944) edition. MR 1349110
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 104 (1988), 453-457
- MSC: Primary 33A40
- DOI: https://doi.org/10.1090/S0002-9939-1988-0962812-X
- MathSciNet review: 962812