where L is a certain contour separating the poles of the two factors in the numerator. Another generalization of Fox H-function is given by Innayat Hussain AA (1987). For a further generalization of this function, useful in Physics and Statistics, see Rathie (1997).
The special case for which the Fox H-function reduces to the Meijer G-function is Aj = Bk = C, C > 0 for j = 1...p and k = 1...q (Srivastava 1984, p. 50):
- Fox, Charles (1961), "The G and H functions as symmetrical Fourier kernels", Transactions of the American Mathematical Society 98: 395–429, ISSN 0002-9947, JSTOR 1993339, MR 0131578
- Innayat-Hussain, AA (1987), "New properties of hypergeometric series derivable from Feynman integrals. I: Transformation and reduction formulae", J. Phys. A: Math. Gen. 20: 4109–4117
- Innayat-Hussain, AA (1987), "New properties of hypergeometric series derivable from Feynman integrals. II: A generalization of the H-function", J. Phys. A: Math. Gen. 20: 4119–4128
- Mathai, A. M.; Saxena, Ram Kishore (1978), The H-function with applications in statistics and other disciplines, Halsted Press [John Wiley & Sons], New York-London-Sidney, ISBN 978-0-470-26380-8, MR 513025
- Mathai, A. M.; Saxena, Ram Kishore; Haubold, Hans J. (2010), The H-function, Berlin, New York: Springer-Verlag, ISBN 978-1-4419-0915-2, MR 2562766
- Rathie, Arjun K. (1997), "A new generalization of generalized hypergeometric function", Le Matematiche LII: 297–310.
- Srivastava, H. M.; Gupta, K. C.; Goyal, S. P. (1982), The H-functions of one and two variables, New Delhi: South Asian Publishers Pvt. Ltd., MR 691138
- Srivastava, H. M.; Manocha, H. L. (1984). A treatise on generating functions. ISBN 0-470-20010-3.
|This mathematical analysis–related article is a stub. You can help Wikipedia by expanding it.|