Sinc Numeric Methods for Fox-H, Aleph (<i>ℵ</i>), and Saxena-I Functions

• 發表在: Fractal and Fractional
• Main Authors: Gerd Baumann, Norbert Südland
• 格式: Article
• 語言: 英语
• 出版: MDPI AG 2022-08-01
• 主題: Mellin-Barnes integrals; Sinc methods; Sinc quadrature; Fox functions; Aleph functions; Saxena function
• 在線閱讀: https://www.mdpi.com/2504-3110/6/8/449
• ISSN: 2504-3110

The purpose of this study is to offer a systematic, unified approach to the Mellin-Barnes integrals and associated special functions as Fox <i>H</i>, Aleph <i>ℵ</i>, and Saxena <i>I</i> function, encompassing the fundamental features and important conclusions under natural minimal assumptions on the functions in question. The approach’s pillars are the concept of a Mellin-Barnes integral and the Mellin representation of the given function. A Sinc quadrature is used in conjunction with a Sinc approximation of the function to achieve the numerical approximation of the Mellin-Barnes integral. The method converges exponentially and can handle endpoint singularities. We give numerical representations of the Aleph <i>ℵ</i> and Saxena <i>I</i> functions for the first time.