Journals Information
Mathematics and Statistics Vol. 13(1), pp. 68 - 74
DOI: 10.13189/ms.2025.130109
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Infinite Integrals with Spheroidal Functions: A Comprehensive Exploration Utilizing Fox's H-Function
A.K. Awasthi , Ruby Kumari *, Lukman Ahmed
Department of Mathematics, School of Chemical Engineering and Physical Sciences, Lovely Professional University, Phagwara, Punjab 144411, India
ABSTRACT
This study investigates six infinite integrals, focusing on their evaluation through the integration of spheroidal functions and Fox's H-function, as introduced by C. Fox. The research aims to expand the analytical approaches available for handling complex integrals involving special functions. By presenting a generalized framework, the study encapsulates several unique cases, including integrals incorporating spheroidal wave functions, Mathieu functions, and the multivariate H-function. A compact representation of the multivariate H-function is introduced, enhancing the mathematical toolkit for subsequent research. Methodologically, this work employs advanced mathematical techniques, including Fox's H-function, contour integration, and established properties of Bessel functions and spheroidal functions, leading to intricate expressions with broad applications. The derived results are applicable to a diverse range of integrals, encompassing modified Bessel functions, spheroidal functions, and parameters that extend the relevance of this analysis to various fields. This research not only emphasizes novel aspects of Fox's H-function but also addresses the limitations in previous frameworks by providing a more flexible and inclusive approach. Potential implications of this work include new insights for mathematical and physical domains that rely on complex integral evaluations, while also presenting practical and theoretical contributions that could inspire further exploration of Fox's H-function applications.
KEYWORDS
Infinite Integrals, Spheroidal Functions, Fox's H-Function, Bessel Function, Gamma Function
Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] A.K. Awasthi , Ruby Kumari , Lukman Ahmed , "Infinite Integrals with Spheroidal Functions: A Comprehensive Exploration Utilizing Fox's H-Function," Mathematics and Statistics, Vol. 13, No. 1, pp. 68 - 74, 2025. DOI: 10.13189/ms.2025.130109.
(b). APA Format:
A.K. Awasthi , Ruby Kumari , Lukman Ahmed (2025). Infinite Integrals with Spheroidal Functions: A Comprehensive Exploration Utilizing Fox's H-Function. Mathematics and Statistics, 13(1), 68 - 74. DOI: 10.13189/ms.2025.130109.