A family of hypergeometric integrals associated with Ramanujan's integral formula
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The main object of this paper is to investigate some interesting applications and generalizations of Ramanujan’s integral formula (which he obtained with the help of the celebrated Ramanujan Master Theorem). Motivated essentially by some recent works by M. Garg and S. Mittal (see, for example, [South East Asian J. Math. Math. Sci. 1 (2) (2003), 85–95]), we evaluate several general families of definite integrals involving functions of one and more complex variables, some of which are then applied to derive the corresponding results associated with the generalized hypergeometric function pFq and the Fox-Wright further generalizations denoted by p[수식]q and p[수식]q . An integral formula considered recently by R. P. Agarwal [Resonance of Ramanujan’s Mathematics, Vol. I, New Age International Publishers Limited, New Delhi, 1996], which is closely associated with the aforementioned Ramanujan’s result, is also corrected and modified here appropriately.
Abstract
The main object of this paper is to investigate some interesting applications and generalizations of Ramanujan’s integral formula (which he obtained with the help of the celebrated Ramanujan Master Theorem). Motivated essentially by some recent works by M. Garg and S. Mittal (see, for example, [South East Asian J. Math. Math. Sci. 1 (2) (2003), 85–95]), we evaluate several general families of definite integrals involving functions of one and more complex variables, some of which are then applied to derive the corresponding results associated with the generalized hypergeometric function pFq and the Fox-Wright further generalizations denoted by p[수식]q and p[수식]q . An integral formula considered recently by R. P. Agarwal [Resonance of Ramanujan’s Mathematics, Vol. I, New Age International Publishers Limited, New Delhi, 1996], which is closely associated with the aforementioned Ramanujan’s result, is also corrected and modified here appropriately.
참고문헌 (15)
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