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2012•The Pure and Applied MathematicsOpen access

INTEGRAL REPRESENTATIONS FOR SRIVASTAVA'S HYPERGEOMETRIC FUNCTION HB

Junesang Choi, Anvar Hasanov, Mamasali Turaev

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Abstract

While investigating the Lauricella's list of 14 complete second-order hypergeometric series in three variables, Srivastava noticed the existence of three additional complete triple hypergeometric series of the second order, which were denoted by $H_A$ , $H_B$ and $H_C$ . Each of these three triple hypergeometric functions $H_A$ , $H_B$ and $H_C$ has been investigated extensively in many different ways including, for example, in the problem of finding their integral representations of one kind or the other. Here, in this paper, we aim at presenting further integral representations for the Srivatava's triple hypergeometric function $H_B$ .

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While investigating the Lauricella's list of 14 complete second-order hypergeometric series in three variables, Srivastava noticed the existence of three additional complete triple hypergeometric series of the second order, which were denoted by $H_A$ , $H_B$ and $H_C$ . Each of these three triple hypergeometric functions $H_A$ , $H_B$ and $H_C$ has been investigated extensively in many different ways including, for example, in the problem of finding their integral representations of one kind or the other. Here, in this paper, we aim at presenting further integral representations for the Srivatava's triple hypergeometric function $H_B$ .

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Available abstract

While investigating the Lauricella's list of 14 complete second-order hypergeometric series in three variables, Srivastava noticed the existence of three additional complete triple hypergeometric series of the second order, which were denoted by $H_A$ , $H_B$ and $H_C$ . Each of these three triple hypergeometric functions $H_A$ , $H_B$ and $H_C$ has been investigated extensively in many different ways including, for example, in the problem of finding their integral representations of one kind or the other. Here, in this paper, we aim at presenting further integral representations for the Srivatava's triple hypergeometric function $H_B$ .

Key concepts: Generalized hypergeometric function, Basic hypergeometric series, Mathematics, Lauricella hypergeometric series, Hypergeometric function, Hypergeometric identity, Appell series, Confluent hypergeometric function

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