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On certain integrals of Lipschitz-Hankel type involving products of bessel functions
Abstract
This paper is concerned with the evaluation and tabulation of certain integrals of the type (* 00 I(p, v; A) = J J fa t) ) e~cttxdt. In part I of this paper, a formula is derived for the integrals in terms of an integral of a hypergeometric function. This new integral is evaluated in the particular cases which are of most frequent use in mathematical physics. By means of these results, approximate expansions are obtained for cases in which the ratio b/a is small or in which b~a and is small. In part II, recurrence relations are developed between integrals with integral values of the parameters pt, v and A. Tables are given by means of which 7(0, 0; 1), 7(0, 1; 1), 7(1, 0; 1), 7(1,1; 1), 7(0, 0 ;0), 7(1, 0;'0), 7(0, 1; 0), 7(1, 1; 0), 7(0,1; - 1 ), 7(1,0; - 1 ) and 7(1,1; - 1 ) may be evaluated for 0 < b/a ^ 2, 0 ^ c/a ^ 2.
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Metadata
- Authors
- Eason, G., Noble, B., & Sneddon, I. N.
- Venue
- Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
- Publisher
- The Royal Society
- Published
- 1955-04-19
- Volume
- 247
- Issue
- 935
- Pages
- 529-551
- ISSN
- 0080-4614 (ISSN-L)
- 2054-0272
- OpenAlex
- W2060422862
- Cited by
- 4,410
- References
- 0
- FWCI
- 0.00
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: On certain integrals of Lipschitz-Hankel type involving products of bessel functions. https://app.cochat.ai/papers/10.1098/rsta.1955.0005
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- Eason, G., Noble, B., & Sneddon, I. N. (1955). On certain integrals of Lipschitz-Hankel type involving products of bessel functions. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences. https://doi.org/10.1098/rsta.1955.0005
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