New bilateral type generating function associated with \(I\)-function. (English) Zbl 1470.33014

Summary: We aim at establishing a new bilateral type generating function associated with the \(I\)-function and a Mellin-Barnes type of contour integral. The results derived here are of general character and can yield a number of (known and new) results in the theory of generating functions.


33C60 Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions)
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[1] Agarwal, P.; Koul, C. L., On generating functions, Journal of Rajasthan Academy of Physical Sciences, 2, 3, 173-180 (2003) · Zbl 1137.33309
[2] Srivastava, H. M., A class of bilateral generating functions for the Jacobi polynomial, Journal of the Korean Mathematical Society, 8, 25-30 (1971) · Zbl 0224.33015
[3] Srivastava, H. M.; Manocha, H. L., A Treatise on Generating Functions (1984), Brisban and Toronto, Canada: Halsted Press (Ellis Horwood), John Wiley & Sons, New York, NY, USA, Chichester, UK, Brisban and Toronto, Canada · Zbl 0535.33001
[4] Srivastava, H. M.; Panda, R., Some bilateral generating functions for a class of generalized hypergeometric polynomials, Journal für die Reine und Angewandte Mathematik, 283/284, 265-274 (1976) · Zbl 0315.33003
[5] Choi, J.; Agarwal, P., Certain generating functions involving Appell series, Far East Journal of Mathematical Sciences, 84, 1, 25-32 (2014) · Zbl 1298.33023
[6] Fox, C., The \(G\) and \(H\) functions as symmetrical Fourier kernels, Transactions of the American Mathematical Society, 98, 395-429 (1961) · Zbl 0096.30804
[7] Braaksma, B. L. J., Asymptotic expansions and analytic continuations for a class of Barnes-integrals, Compositio Mathematica, 15, 239-341 (1964) · Zbl 0129.28604
[8] Saxena, V. P., A formal solution of certain new pair of dual integral equations involving Hfunctions, Proceedings of the National Academy of Science of India A, 52, 366-375 (1982) · Zbl 0535.45001
[9] Saxena, V. P., The I-Function (2008), New Delhi, India: Anamaya, New Delhi, India
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