Evaluation of the integral

Author:
Paul W. Schmidt

Journal:
Math. Comp. **32** (1978), 265-269

MSC:
Primary 33A35

MathSciNet review:
0457812

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Abstract | References | Similar Articles | Additional Information

Abstract: Methods are developed for evaluating the integral

The are shown to be proportional to a *G* function. From this result, power series expansions and recurrence relations are developed for use in evaluating the . A convenient expression is obtained for the quantity required in Fedorova's method for computing diameter distributions.

**[1]**I. S. FEDOROVA,*Dokl. Akad. Nauk SSSR*, v. 223, 1975, p. 1007.**[2]**I. S. FEDOROVA & J. COLLOID,*Interface Sci.*, v. 59, 1977, pp. 100-101.**[3]**W. MAGNUS & F. OBERHETTINGER,*Formulas and Theorems for the Functions of Mathematical Physics*, Chelsea, New York, 1954, p. 32.**[4]**Yudell L. Luke,*The special functions and their approximations, Vol. I*, Mathematics in Science and Engineering, Vol. 53, Academic Press, New York-London, 1969. MR**0241700****[5]**Ref. 4, p. 226, Eq. (7).**[6]**Ref. 4, p. 170, Eq. (6).**[7]**Ref. 4, p. 145, Eq. (7).**[8]**Ref. 4, pp. 11-13.**[9]**Ref. 4, pp. 143-144.**[10]**Ref. 4, p. 229, Eq. (30).**[11]**G. N. Watson,*A treatise on the theory of Bessel functions*, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1995. Reprint of the second (1944) edition. MR**1349110****[12]**Ref. 11, p. 77, Eq. (12).

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DOI:
https://doi.org/10.1090/S0025-5718-1978-0457812-4

Article copyright:
© Copyright 1978
American Mathematical Society