Generalized gamma-type functions involving Kummer’s confluent hypergeometric function and associated probability distributions

Saxena, R. K.; Ram, Chena; Dudi, Naresh; Kalla, S. L.

doi:10.1080/10652460701510501

Cited by 2 publications

(2 citation statements)

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“…A lot of research work has recently come up on the study and development of a function that is more general than the Fox H-function (see, e.g., [10,11]), popularly known as H-function. It was introduced by Inayat-Hussain [6,7] and now stands on a fairly firm footing through the following contributions of various authors [3,4,6,7,9,10].…”

Section: Definition and Existence Conditions Of H-functionmentioning

confidence: 99%

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Certain Classes of Infinite Series Deducible From Mellin-Barnes Type of Contour Integrals

Choi¹,

Agarwal²

2013

The Pure and Applied Mathematics

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Abstract. Certain interesting single (or double) infinite series associated with hypergeometric functions have been expressed in terms of Psi (or Digamma) function ψ(z), for example, see Nishimoto and Srivastava [8], Srivastava and Nishimoto [13], Saxena [10], and Chen and Srivastava [5], and so on. In this sequel, with a view to unifying and extending those earlier results, we first establish two relations which some double infinite series involving hypergeometric functions are expressed in a single infinite series involving ψ(z). With the help of those series relations we derived, we next present two functional relations which some double infinite series involving H-functions, which are defined by a generalized Mellin-Barnes type of contour integral, are expressed in a single infinite series involving ψ(z). The results obtained here are of general character and only two of their special cases, among numerous ones, are pointed out to reduce to some known results.

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