Extended beta, hypergeometric and confluent hypergeometric functions via multi-index mittag-leffler function
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In this paper, we first introduce an interesting generalization of the well-known beta function by means of a multi-index Mittag-Leffler function and study its important properties. We establish several new representations of the extended beta function, which shows explicit connections with other special functions. With the help of this new beta function, we introduce extensions of generalized hypergeometric function and confluent hypergeometric functions. Consequently, we present a systematic study of the fundamental properties of an extended hypergeometric function introduced here.
Abstract
In this paper, we first introduce an interesting generalization of the well-known beta function by means of a multi-index Mittag-Leffler function and study its important properties. We establish several new representations of the extended beta function, which shows explicit connections with other special functions. With the help of this new beta function, we introduce extensions of generalized hypergeometric function and confluent hypergeometric functions. Consequently, we present a systematic study of the fundamental properties of an extended hypergeometric function introduced here.
참고문헌 (16)
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