The author evaluates certain integrals of the form
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, . The results can be deduced from the known integrals involving hypergeometric functions [A. Erdélyi et al.: Higher transcendental functions. II (1953; Zbl 0052.295)]. 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.
Generalized elliptic-type integrals have been considered by L. F. Epstein and J. H. Hubbell [ibid. 67, 1-17 (1963; Zbl 0114.064)], the reviewer, S. Conde and J. H. Hubbell [Appl. Anal. 22, 273-287 (1986; Zbl 0588.33001)], the reviewer, C. Leubner and J. H. Hubbell [Appl. Anal. 25, 269-274 (1987; Zbl 0606.33003)] and the reviewer and B. Al-Saqabi [Rev. Bras. Fisica 16, 145-156 (1986; Zbl 0597.33004)].