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Zbl 0628.33002
Bushell, P.J.
On a generalization of Barton's integral and related integrals of complete elliptic integrals. (English)
[J] Math. Proc. Camb. Philos. Soc. 101, 1-5 (1987). ISSN 0305-0041; ISSN 1469-8064/e

The author evaluates certain integrals of the form $$ \int\sp{1}\sb{0}k\sp{\mu} f(k)dk, $$ where f(k) is replaced by K(k), E(k), K(k') and E(k'), the complete elliptic integrals of the first and second kind respectively, $k'=\sqrt{(1-k\sp 2)}$. The results can be deduced from the known integrals involving hypergeometric functions [{\it A. Erdélyi} et al.: Higher transcendental functions. II (1953; Zbl 0052.295)]. {\it M. L. Glasser} [J. Res. Natl. Bur. Stand., Sect. B 80, 313- 323 (1976; Zbl 0339.33001)] has given an extensive table of definite integrals of the complete elliptic integral K. \par Generalized elliptic-type integrals have been considered by {\it L. F. Epstein} and {\it J. H. Hubbell} [ibid. 67, 1-17 (1963; Zbl 0114.064)], the reviewer, {\it S. Conde} and {\it J. H. Hubbell} [Appl. Anal. 22, 273-287 (1986; Zbl 0588.33001)], the reviewer, {\it C. Leubner} and {\it J. H. Hubbell} [Appl. Anal. 25, 269-274 (1987; Zbl 0606.33003)] and the reviewer and {\it B. Al-Saqabi} [Rev. Bras. Fisica 16, 145-156 (1986; Zbl 0597.33004)].
[S.L.Kalla]

MSC 2000:: *33E05 Elliptic functions and integrals
33C05 Classical hypergeometric functions

Keywords: elliptic-type integrals

Citations: Zbl 0597.33005; Zbl 0619.33001; Zbl 0052.295; Zbl 0339.33001; Zbl 0114.064; Zbl 0588.33001; Zbl 0606.33003; Zbl 0597.33004

Cited in: Zbl 0858.33017

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