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On Stieltjes integral transforms involving $ \Gamma $-functions


Authors: V. Belevitch and J. Boersma
Journal: Math. Comp. 38 (1982), 223-226
MSC: Primary 44A15; Secondary 33A15, 33A45
DOI: https://doi.org/10.1090/S0025-5718-1982-0637300-3
MathSciNet review: 637300
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Abstract: After some methodological remarks on the theory of Stieltjes transforms, a systematic classification of transforms involving $ \Gamma $-functions is presented As a consequence, many new transforms are established and much simpler proofs for a few known transforms are obtained.


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

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  • [2] V. Belevitch, ``The Gauss hypergeometric ratio as a positive real function,'' SIAM J. Math. Anal. (Submitted.) MR 674771 (83k:33002)
  • [3] V. Belevitch & J. Boersma, ``The Bessel ratio $ {K_{\nu + 1}}(z)/{K_\nu }(z)$ as a passive impedance,'' Philips J. Res., v. 34, 1979, pp. 163-173. MR 546260 (80f:94032)
  • [4] A. Erdélyi et al., Tables of Integral Transforms, Vol. 2, McGraw-Hill, New York, 1954.
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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1982-0637300-3
Article copyright: © Copyright 1982 American Mathematical Society

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