Evaluation of Howland-type integrals involving and functions

Author:
Chih-Bing Ling

Journal:
Math. Comp. **46** (1986), 219-223

MSC:
Primary 65A05; Secondary 65D20

MathSciNet review:
815843

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Abstract | References | Similar Articles | Additional Information

Abstract: Four Howland-type integrals involving tanh and coth functions in their integrands are evaluated in this paper. The results are tabulated to 20D.

**[1]**J. W. L. Glaisher, "Tables of etc. and etc., to 32 places of decimals,"*Quart. J. Math.*, v. 45, 1914, pp. 141-158. The tables are reproduced in H. T. Davies,*Tables of Higher Mathematical Functions*, vol. 2, Principia Press, Bloomington, Indiana, 1955.**[2]**Chih-Bing Ling,*Tables of values of 16 integrals of algebraic-hyperbolic type*, Math. Tables Aids Comput.**11**(1957), 160–166. MR**0090892**, 10.1090/S0025-5718-1957-0090892-3**[3]**Chih Bing Ling and Jung Lin,*A new method of evaluation of Howland integrals*, Math. Comp.**25**(1971), 331–337. MR**0295537**, 10.1090/S0025-5718-1971-0295537-2**[4]**Chih Bing Ling,*Further evaluation of Howland integrals*, Math. Comp.**32**(1978), no. 143, 900–904. MR**492047**, 10.1090/S0025-5718-1978-0492047-0**[5]**Chih Bing Ling and Ming Jing Wu,*Evaluation of integrals of Howland type involving a Bessel function*, Math. Comp.**38**(1982), no. 157, 215–222. MR**637299**, 10.1090/S0025-5718-1982-0637299-X

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DOI:
http://dx.doi.org/10.1090/S0025-5718-1986-0815843-0

Keywords:
Howland integrals,
Howland-type integrals

Article copyright:
© Copyright 1986
American Mathematical Society