On Certain Integrals Related to Saran’s Hypergeometric Function <i>F<sub>K</sub></i>
In the present paper, we establish two Erdélyi-type integrals for Saran’s hypergeometric function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>F</mi><mi>K</mi></msub>&l...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-03-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/3/155 |
| _version_ | 1797471527043596288 |
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| author | Minjie Luo Minghui Xu Ravinder Krishna Raina |
| author_facet | Minjie Luo Minghui Xu Ravinder Krishna Raina |
| author_sort | Minjie Luo |
| collection | DOAJ |
| description | In the present paper, we establish two Erdélyi-type integrals for Saran’s hypergeometric function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>F</mi><mi>K</mi></msub></semantics></math></inline-formula>, which has applications in specific branches of applied physics and statistics (see below). We employ methods based on the <i>k</i>-dimensional fractional integration by parts to obtain our main integral identities. The first integral generalizes Koschmieder’s result and the second integral extends one of Erdélyi’s classical hypergeometric integral. Some useful special cases and important remarks are also discussed. |
| first_indexed | 2024-03-09T19:49:26Z |
| format | Article |
| id | doaj.art-9d15cd6196aa4a38b8e69ad4fc173127 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T19:49:26Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-9d15cd6196aa4a38b8e69ad4fc1731272023-11-24T01:14:34ZengMDPI AGFractal and Fractional2504-31102022-03-016315510.3390/fractalfract6030155On Certain Integrals Related to Saran’s Hypergeometric Function <i>F<sub>K</sub></i>Minjie Luo0Minghui Xu1Ravinder Krishna Raina2Department of Mathematics, College of Science, Donghua University, Shanghai 201620, ChinaDepartment of Mathematics, College of Science, Donghua University, Shanghai 201620, ChinaDepartment of Mathematics, College of Technology & Engineering, Maharana Pratap University of Agriculture and Technology, Udaipur 313001, IndiaIn the present paper, we establish two Erdélyi-type integrals for Saran’s hypergeometric function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>F</mi><mi>K</mi></msub></semantics></math></inline-formula>, which has applications in specific branches of applied physics and statistics (see below). We employ methods based on the <i>k</i>-dimensional fractional integration by parts to obtain our main integral identities. The first integral generalizes Koschmieder’s result and the second integral extends one of Erdélyi’s classical hypergeometric integral. Some useful special cases and important remarks are also discussed.https://www.mdpi.com/2504-3110/6/3/155Erdélyi-type integralfractional integration by partsSaran’s function |
| spellingShingle | Minjie Luo Minghui Xu Ravinder Krishna Raina On Certain Integrals Related to Saran’s Hypergeometric Function <i>F<sub>K</sub></i> Fractal and Fractional Erdélyi-type integral fractional integration by parts Saran’s function |
| title | On Certain Integrals Related to Saran’s Hypergeometric Function <i>F<sub>K</sub></i> |
| title_full | On Certain Integrals Related to Saran’s Hypergeometric Function <i>F<sub>K</sub></i> |
| title_fullStr | On Certain Integrals Related to Saran’s Hypergeometric Function <i>F<sub>K</sub></i> |
| title_full_unstemmed | On Certain Integrals Related to Saran’s Hypergeometric Function <i>F<sub>K</sub></i> |
| title_short | On Certain Integrals Related to Saran’s Hypergeometric Function <i>F<sub>K</sub></i> |
| title_sort | on certain integrals related to saran s hypergeometric function i f sub k sub i |
| topic | Erdélyi-type integral fractional integration by parts Saran’s function |
| url | https://www.mdpi.com/2504-3110/6/3/155 |
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