On the dual valued generalized hypergeometric function and its special cases

2025/07/10 by Dwivedi, Ravi, Cortés, Juan Carlos
#FOS: Mathematics #General Mathematics (math.GM)

paper · doi:10.48550/arxiv.2507.19501

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.

Citations

• A dual number formulation to efficiently compute higher order directional derivatives
• TensorFlow: A system for large-scale machine learning
• Differential Geometry, Lie Groups and Symmetric Spaces over General Base Fields and Rings
• Preliminary Sketch of Biquaternions

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