{"id":13988,"date":"2025-07-10T20:17:14","date_gmt":"2025-07-10T19:17:14","guid":{"rendered":"https:\/\/icertpublication.com\/?page_id=13988"},"modified":"2025-07-10T20:28:57","modified_gmt":"2025-07-10T19:28:57","slug":"a-study-of-generalized-hypergeometric-function-and-its-applications-in-vary-disciplines","status":"publish","type":"page","link":"https:\/\/icertpublication.com\/index.php\/shodh-sari-2\/hodh-sari-an-international-multidisciplinary-journal-vol-04-issue-02-apr-jun-2025\/a-study-of-generalized-hypergeometric-function-and-its-applications-in-vary-disciplines\/","title":{"rendered":"A Study of Generalized Hypergeometric Function and its Applications in Vary Disciplines"},"content":{"rendered":"\t\t
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A Study of Generalized Hypergeometric Function and its Applications in\nVary Disciplines<\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Mahala, Mukesh Kumar<\/span>1 <\/span><\/span>and Sharma, Rahul<\/span>2<\/span><\/span><\/p>

1<\/span><\/span>Department of Mathematics, University of Engineering & Management Jaipur, Jaipur, Rajasthan, India<\/span><\/p>

2<\/span><\/span>Department of Mathematics, Seth Gyaniram Bansidhar Podar College, Nawalgarh, Rajasthan, India<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Abstract\n<\/h6>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Elementary functions, Bessel functions, Legendre functions and many other special functions are included in the large family of mathematical functions known as generalized hypergeometric functions. A power series with coefficients that are rational functions of the index defines them. They are used in many disciplines, such as engineering, statistics and physics, because of their rich mathematical features and adaptability. The beauty and interdependence of mathematical ideas are demonstrated by the Generalized Hypergeometric Function. Researchers and practitioners from a wide range of disciplines find it to be an indispensable tool due to its unifying power, rich analytical features, and broad applications. Numerous unusual functions are included as particular examples of the generalized Hypergeometric function. Legendre polynomials, Bessel functions, the confluent Hypergeometric function, and numerous more noteworthy examples are also included. An order <\/span>(q+1)<\/span> linear homogeneous differential equation is satisfied by the generalized hypergeometric function. In many applications, but especially in mathematical physics, this differential equation is essential. It is possible to write the generalized hypergeometric function in terms of contour integrals, which offers different representations and makes it easier to evaluate some integrals. The generalized Hypergeometric function has a wealth of transformation formulas that allow one Hypergeometric function to be transformed into another with distinct parameters. These transformations are quite useful for examining relationships between various special functions and simplifying expressions.<\/span><\/p>

Keywords<\/span>: Special Function, Generalized Hypergeometric functions, Recurrence Relations<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Impact Statement\n<\/h6>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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This study investigates the generalized hypergeometric function, a powerful and unifying mathematical tool that encompasses a wide range of special and elementary functions. By establishing novel representations and transformation identities, the work enhances understanding of the hypergeometric function\u2019s role in solving complex differential equations, particularly those arising in physical models and computational mathematics. The ability to express numerous classical functions\u2014like Legendre, Bessel, and trigonometric functions\u2014as special cases of the generalized hypergeometric function provides a cohesive framework for theoretical and applied investigations. This contributes to both the simplification of mathematical modelling and the development of efficient computational methods.\u00a0<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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About Author\n<\/h6>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Mr. Mukesh Kumar Mahala is a dedicated academic professional with over 9 years of teaching experience in mathematics at the postgraduate level. He is currently serving as an Assistant Professor at Shri Shraddhanath P.G. College, Jhunjhunu. He has previously held similar roles at Shekhawati P.G. College, Sikar, and Shri Narayan P.G. College, Jaipur. He holds an M.Sc. in Mathematics and a B.Ed. and is presently pursuing a PhD from the University of Engineering & Management, Jaipur.<\/span><\/p>

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Dr. Rahul Sharma is currently serving as Associate Professor and Head of the Department of Mathematics at the University of Engineering & Management, Jaipur, with over 13 years of teaching and research experience. He holds a Ph.D. in Mathematics from Amity University Rajasthan, specializing in special functions. Dr. Sharma has published extensively in Scopus and ESCI-indexed journals and actively contributes to academic conferences.\u00a0<\/span><\/p>

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Dr. Vidyadhar Sharma’s primary research interests lie in the fields of Applied & Pure Mathematics, with a specific focus on Fractional Calculus and Special Functions. His work includes studies on subclasses of analytic functions, bi-univalent functions, meromorphic functions, and applications of fractional integral operators.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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References<\/h6>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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\u00a0<\/p>

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  6. Arshad, M., Mubeen, S., Nisar, K. S., & Rahman, G. (2018). Extended Wright\u2013Bessel function and its properties. <\/span>Communications of the Korean Mathematical Society<\/span>, <\/span>33<\/span>(1), 143\u2013155.<\/span><\/p><\/li>

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  9. Chaudhry, M. A., Qadir, A., Srivastava, H. M., & Paris, R. B. (2004). Extended hypergeometric and confluent hypergeometric functions. <\/span>Applied Mathematics and Computation<\/span>, <\/span>159<\/span>(2)(2), 589\u2013602. <\/span>https:\/\/doi.org\/10.1016\/j.amc.2003.09.017<\/span><\/a><\/p><\/li>

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  11. Kumar, S., & Simran, S. (2024). Psychological impact of physical distancing due to covid 19 pandemic on school and higher education students. <\/span>Edumania-An International Multidisciplinary Journal<\/span>, <\/span>02<\/span>(04), 101\u2013112. https:\/\/doi.org\/10.59231\/edumania\/9076<\/span><\/p><\/li>

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  13. Choi, J., Rathie, A. K., & Parmar, R. K. (2014). Extension of extended beta, hypergeometric and confluent hypergeometric functions. <\/span>Honam Mathematical Journal<\/span>, <\/span>36<\/span>(2)(2), 357\u2013385. <\/span>https:\/\/doi.org\/10.5831\/HMJ.2014.36.2.357<\/span><\/a><\/p><\/li>

  14. Dragovic, V. (2002). The Appell hypergeometric functions and classical separable mechanical systems. <\/span>Journal of Physics A<\/span>, <\/span>35<\/span>(9)(9), 2213\u20132221. <\/span>https:\/\/doi.org\/10.1088\/0305-4470\/35\/9\/311<\/span><\/a><\/p><\/li>

  15. Galu\u00e9, L., Al-Zamel, A., & Kalla, S. L. (2003). Further results on generalized hypergeometric functions. <\/span>Applied Mathematics and Computation<\/span>, <\/span>136<\/span>(1)(1), 17\u201325. <\/span>https:\/\/doi.org\/10.1016\/S0096-3003(02)00014-0<\/span><\/a><\/p><\/li>

  16. Koekoek, R., Lesky, P. A., & Swarttouw, R. F. (2010). Hypergeometric orthogonal polynomials and their\u00a0<\/span>q<\/span>-analogues. <\/span>Springer Monographs in Mathematics<\/span>. Springer.<\/span><\/p><\/li><\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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    A Study of Generalized Hypergeometric Function and its Applications in Vary Disciplines Mahala, Mukesh Kumar1 and Sharma, Rahul2 1Department of Mathematics, University of Engineering & Management Jaipur, Jaipur, Rajasthan, India 2Department of Mathematics, Seth Gyaniram Bansidhar Podar College, Nawalgarh, Rajasthan, India Abstract Elementary functions, Bessel functions, Legendre functions and many other special functions are included […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":13912,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"site-sidebar-layout":"no-sidebar","site-content-layout":"page-builder","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"disabled","ast-breadcrumbs-content":"","ast-featured-img":"disabled","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"class_list":["post-13988","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/icertpublication.com\/index.php\/wp-json\/wp\/v2\/pages\/13988","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/icertpublication.com\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/icertpublication.com\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/icertpublication.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/icertpublication.com\/index.php\/wp-json\/wp\/v2\/comments?post=13988"}],"version-history":[{"count":7,"href":"https:\/\/icertpublication.com\/index.php\/wp-json\/wp\/v2\/pages\/13988\/revisions"}],"predecessor-version":[{"id":13999,"href":"https:\/\/icertpublication.com\/index.php\/wp-json\/wp\/v2\/pages\/13988\/revisions\/13999"}],"up":[{"embeddable":true,"href":"https:\/\/icertpublication.com\/index.php\/wp-json\/wp\/v2\/pages\/13912"}],"wp:attachment":[{"href":"https:\/\/icertpublication.com\/index.php\/wp-json\/wp\/v2\/media?parent=13988"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}