Certain Identities Involving the General Kampé de Fériet Function and Srivastava’s General Triple Hypergeometric Series
Due to the great success of hypergeometric functions of one variable, a number of hypergeometric functions of two or more variables have been introduced and explored. Among them, the Kampé de Fériet function and its generalizations have been actively researched and applied. The aim of this paper is...
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MDPI AG
2022-11-01
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| author | Mohd Idris Qureshi Junesang Choi Mohd Shaid Baboo |
| author_facet | Mohd Idris Qureshi Junesang Choi Mohd Shaid Baboo |
| author_sort | Mohd Idris Qureshi |
| collection | DOAJ |
| description | Due to the great success of hypergeometric functions of one variable, a number of hypergeometric functions of two or more variables have been introduced and explored. Among them, the Kampé de Fériet function and its generalizations have been actively researched and applied. The aim of this paper is to provide certain reduction, transformation and summation formulae for the general Kampé de Fériet function and Srivastava’s general triple hypergeometric series, where the parameters and the variables are suitably specified. The identities presented in the theorems and additional comparable outcomes are hoped to be supplied by the use of computer-aid programs, for example, Mathematica. Symmetry occurs naturally in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow></mrow><mrow><mi>p</mi><mo>+</mo><mn>1</mn></mrow></msub><msub><mi>F</mi><mi>p</mi></msub></mrow></semantics></math></inline-formula>, the Kampé de Fériet function and the Srivastava’s function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>F</mi><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow></msup><mrow><mo>[</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>]</mo></mrow></mrow></semantics></math></inline-formula>, which are three of the most important functions discussed in this study. |
| first_indexed | 2024-03-09T15:48:49Z |
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| language | English |
| last_indexed | 2024-03-09T15:48:49Z |
| publishDate | 2022-11-01 |
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| series | Symmetry |
| spelling | doaj.art-8b8918988e4a413dac3ed6c7aefd82ed2023-11-24T18:18:52ZengMDPI AGSymmetry2073-89942022-11-011412250210.3390/sym14122502Certain Identities Involving the General Kampé de Fériet Function and Srivastava’s General Triple Hypergeometric SeriesMohd Idris Qureshi0Junesang Choi1Mohd Shaid Baboo2Department of Applied Sciences and Humanities, Faculty of Engineering and Technology, Jamia Millia Islamia (A Central University), New Delhi 110025, IndiaDepartment of Mathematics, Dongguk University, Gyeongju 38066, Republic of KoreaSchool of Basic Sciences and Research, Sharda University, Greater Noida 201306, IndiaDue to the great success of hypergeometric functions of one variable, a number of hypergeometric functions of two or more variables have been introduced and explored. Among them, the Kampé de Fériet function and its generalizations have been actively researched and applied. The aim of this paper is to provide certain reduction, transformation and summation formulae for the general Kampé de Fériet function and Srivastava’s general triple hypergeometric series, where the parameters and the variables are suitably specified. The identities presented in the theorems and additional comparable outcomes are hoped to be supplied by the use of computer-aid programs, for example, Mathematica. Symmetry occurs naturally in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow></mrow><mrow><mi>p</mi><mo>+</mo><mn>1</mn></mrow></msub><msub><mi>F</mi><mi>p</mi></msub></mrow></semantics></math></inline-formula>, the Kampé de Fériet function and the Srivastava’s function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>F</mi><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow></msup><mrow><mo>[</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>]</mo></mrow></mrow></semantics></math></inline-formula>, which are three of the most important functions discussed in this study.https://www.mdpi.com/2073-8994/14/12/2502Catalan’s constanthypergeometric and generalized hypergeometric functionsRiemann zeta functionDirichlet beta function(general) Kampé de Fériet functionSrivastava’s general triple hypergeometric series |
| spellingShingle | Mohd Idris Qureshi Junesang Choi Mohd Shaid Baboo Certain Identities Involving the General Kampé de Fériet Function and Srivastava’s General Triple Hypergeometric Series Symmetry Catalan’s constant hypergeometric and generalized hypergeometric functions Riemann zeta function Dirichlet beta function (general) Kampé de Fériet function Srivastava’s general triple hypergeometric series |
| title | Certain Identities Involving the General Kampé de Fériet Function and Srivastava’s General Triple Hypergeometric Series |
| title_full | Certain Identities Involving the General Kampé de Fériet Function and Srivastava’s General Triple Hypergeometric Series |
| title_fullStr | Certain Identities Involving the General Kampé de Fériet Function and Srivastava’s General Triple Hypergeometric Series |
| title_full_unstemmed | Certain Identities Involving the General Kampé de Fériet Function and Srivastava’s General Triple Hypergeometric Series |
| title_short | Certain Identities Involving the General Kampé de Fériet Function and Srivastava’s General Triple Hypergeometric Series |
| title_sort | certain identities involving the general kampe de feriet function and srivastava s general triple hypergeometric series |
| topic | Catalan’s constant hypergeometric and generalized hypergeometric functions Riemann zeta function Dirichlet beta function (general) Kampé de Fériet function Srivastava’s general triple hypergeometric series |
| url | https://www.mdpi.com/2073-8994/14/12/2502 |
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