Evaluation of integrals of Howland type involving a Bessel function
HTML articles powered by AMS MathViewer
- by Chih Bing Ling and Ming Jing Wu PDF
- Math. Comp. 38 (1982), 215-222 Request permission
Abstract:
This paper presents a method of evaluation of four integrals of Howland type, which involve a Bessel function in the integrands. With the aid of tabulated values, they are evaluated to 10D. Two of the four Howland integrals needed in the evaluation are evaluated anew to 20D in order to provide adequate accuracy.References
-
A. ErdÉlyi et al., Higher Transcendental Functions, vol. 1, Chapter 3, McGraw-Hill, New York, 1953.
J. W. L. Glaisher, “Tables of $1 \pm {2^{ - n}} + {3^{ - n}} \pm {4^{ - n}} + {\text {etc}}.$, etc. to 32 places of decimals,” Quart. J. Math., v. 45, 1914, pp. 141-158.
K. Knopp, Infinite Series, Hafner, New York, 1947.
- Chih-Bing Ling, Tables of values of $16$ integrals of algebraic-hyperbolic type, Math. Tables Aids Comput. 11 (1957), 160–166. MR 90892, DOI 10.1090/S0025-5718-1957-0090892-3
- Chih Bing Ling, Further evaluation of Howland integrals, Math. Comp. 32 (1978), no. 143, 900–904. MR 492047, DOI 10.1090/S0025-5718-1978-0492047-0
- Chih Bing Ling and Jung Lin, A new method of evaluation of Howland integrals, Math. Comp. 25 (1971), 331–337. MR 295537, DOI 10.1090/S0025-5718-1971-0295537-2
- Yudell L. Luke, Integrals of Bessel functions, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1962. MR 0141801
- C. W. Nelson, New tables of Howland’s and related integrals, Math. Comp. 15 (1961), 12–18. MR 119442, DOI 10.1090/S0025-5718-1961-0119442-0
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Math. Comp. 38 (1982), 215-222
- MSC: Primary 65A05; Secondary 65D20
- DOI: https://doi.org/10.1090/S0025-5718-1982-0637299-X
- MathSciNet review: 637299