A new method of evaluation of Howland integrals

Authors:
Chih Bing Ling and Jung Lin

Journal:
Math. Comp. **25** (1971), 331-337

MSC:
Primary 65D30

DOI:
https://doi.org/10.1090/S0025-5718-1971-0295537-2

MathSciNet review:
0295537

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Abstract: In this paper, two Howland integrals are evaluated to 25D when the index is an odd integer. Those Howland integrals when the index is an even integer have been evaluated to 18D by Nelson. A new method of evaluation is used.

**[1]**R. C. J. Howland, "On the stresses in the neighbourhood of a circular hole in a strip under tension,"*Philos. Trans. Roy. Soc. London Ser. A*, v. 229, 1930, 49-86.**[2]**R. C. J. Howland & A. C. Stevenson, "Biharmonic analysis in a perforated strip,"*Philos. Trans. Roy. Soc. London Ser. A*, v. 232, 1934, pp. 155-222.**[3]**C. B. Ling & C. W. Nelson, "On evaluation of Howland integrals,"*Ann. Acad. Sinica, Taiwan*, v. 2, part 2, 1955, pp. 45-50.**[4]**Chih-Bing Ling,*Tables of values of 16 integrals of algebraic-hyperbolic type*, Math. Tables Aids Comput.**11**(1957), 160–166. MR**90892**, https://doi.org/10.1090/S0025-5718-1957-0090892-3**[5]**C. W. Nelson,*New tables of Howland’s and related integrals*, Math. Comp.**15**(1961), 12–18. MR**119442**, https://doi.org/10.1090/S0025-5718-1961-0119442-0**[6]**A. Erdélyi, et al.,*Higher Transcendental Functions*. Vol. I, McGraw-Hill, New York, 1953, pp. 175-176. MR**15**, 419.**[7]**E. T. Whittaker & G. Robinson,*Calculus of Observations*, 4th ed., Blackie, London, 1948, pp. 143-144.**[8]**C. B. Ling & F. H. Cheng, "Stresses in a semi-infinite strip,"*Internat. J. Engrg. Sci.*, v. 5, 1967, pp. 155-170.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1971-0295537-2

Keywords:
Evaluation of Howland integrals

Article copyright:
© Copyright 1971
American Mathematical Society