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首页> 外文期刊>Turkish Journal of Analysis and Number Theory >A Study of the S-Generalized Gauss Hypergeometric Function and Its Associated Integral Transforms
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A Study of the S-Generalized Gauss Hypergeometric Function and Its Associated Integral Transforms

机译：S广义高斯超几何函数及其相关积分变换的研究

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The aim of the present paper is to further investigate the S-generalized Gauss hypergeometric function which was recently introduced by Srivastava et al. [8]. In the course of our study, we first present an integral representation, the Mellin transform and a complex integral representation of the S-generalized Gauss hypergeometric function. Next, we introduce a new integral transform whose kernel is the S-generalized Gauss hypergeometric function and point out its three special cases which are also believed to be new. We specify that the well-known Gauss hypergeometric function transform follows as a simple special case of our integral transforms. Finally, we establish an inversion formula for the integral transform which we have introduced in this investigation.
机译：本文的目的是进一步研究Srivastava等人最近引入的S广义高斯超几何函数。 [8]。在我们的研究过程中，我们首先呈现S广义Gauss超几何函数的积分表示，Mellin变换和复杂积分表示。接下来，我们介绍一个新的积分变换，其核是S广义高斯超几何函数，并指出它的三个特殊情况，它们也被认为是新的。我们指定遵循众所周知的高斯超几何函数变换作为我们积分变换的简单特殊情况。最后，我们为积分变换建立了一个反演公式。

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