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arXiv · 2507.19501

On the dual valued generalized hypergeometric function and its special cases

Ravi Dwivedi·Juan Carlos Cortés
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Abstract

This paper explores the calculus of dual-valued functions and investigates the gamma function, beta function and generalized hypergeometric functions by incorporating dual numbers as parameters and variables. We examine its fundamental properties, including regions of convergence, differential equations, and integral representations. Furthermore, we provide an in-depth discussion on the various properties of the dual confluent and Gauss hypergeometric functions.

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Ravi Dwivedi, Juan Carlos Cortés. 2025-07-10. On the dual valued generalized hypergeometric function and its special cases. https://arxiv.org/abs/2507.19501

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