Topics in mathematical analysis, Vol. Dedicated Mem. of A. L. Cauchy, Ser. Pure Math. 11, 294-314 (1989).
[For the entire collection see Zbl 0721.00014.]
Various -extensions of the beta-integral and the integrals of Barnes and Cauchy have been deduced in recent years. See, for example, R. Askey and R. Roy [Rocky Mt. J. Math. 16, 365-372 (1986; Zbl 0599.33002)].
Cauchy’s residue theorem and certain summation formulas for - hypergeometric series are used in this study to provide further extensions of the same integrals. Furthermore, various -contour integrals are evaluated and a transformation formula of general character involving -hypergeometric series of one variable is obtained.