Some Incomplete Hypergeometric Functions and Incomplete Riemann-Liouville Fractional Integral Operators
Very recently, the incomplete Pochhammer ratios were defined in terms of the incomplete beta function B y ( x , z ) . With the help of these incomplete Pochhammer ratios, we introduce new incomplete Gauss, confluent hypergeometric, and Appell’s functions and investigate several properties of them su...
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| Vydáno v: | Mathematics (Basel) Ročník 7; číslo 5; s. 483 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Basel
MDPI AG
01.05.2019
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| ISSN: | 2227-7390, 2227-7390 |
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| Abstract | Very recently, the incomplete Pochhammer ratios were defined in terms of the incomplete beta function B y ( x , z ) . With the help of these incomplete Pochhammer ratios, we introduce new incomplete Gauss, confluent hypergeometric, and Appell’s functions and investigate several properties of them such as integral representations, derivative formulas, transformation formulas, and recurrence relations. Furthermore, incomplete Riemann-Liouville fractional integral operators are introduced. This definition helps us to obtain linear and bilinear generating relations for the new incomplete Gauss hypergeometric functions. |
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| AbstractList | Very recently, the incomplete Pochhammer ratios were defined in terms of the incomplete beta function By(x,z). With the help of these incomplete Pochhammer ratios, we introduce new incomplete Gauss, confluent hypergeometric, and Appell’s functions and investigate several properties of them such as integral representations, derivative formulas, transformation formulas, and recurrence relations. Furthermore, incomplete Riemann-Liouville fractional integral operators are introduced. This definition helps us to obtain linear and bilinear generating relations for the new incomplete Gauss hypergeometric functions. Very recently, the incomplete Pochhammer ratios were defined in terms of the incomplete beta function B y ( x , z ) . With the help of these incomplete Pochhammer ratios, we introduce new incomplete Gauss, confluent hypergeometric, and Appell’s functions and investigate several properties of them such as integral representations, derivative formulas, transformation formulas, and recurrence relations. Furthermore, incomplete Riemann-Liouville fractional integral operators are introduced. This definition helps us to obtain linear and bilinear generating relations for the new incomplete Gauss hypergeometric functions. |
| Author | Özarslan, Mehmet Ali Ustaoğlu, Ceren |
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| Cites_doi | 10.1016/S0377-0427(96)00102-1 10.1134/S1061920813010111 10.1201/9781420036046 10.1080/10652469.2011.623350 10.1016/j.amc.2013.10.032 10.1016/j.amc.2014.02.036 10.1115/1.4034460 10.1115/1.4000563 10.2298/FIL1607779C 10.1007/978-1-4020-6042-7 10.2298/FIL1508811L 10.1016/j.mcm.2010.07.011 10.1142/9789812817747 10.1016/B978-0-12-804002-7.00002-4 10.1134/S1061920818010119 10.1016/j.amc.2012.11.050 10.1016/j.cnsns.2018.04.019 10.1016/j.cam.2010.04.019 10.3390/axioms1030238 10.1002/mma.3986 10.1142/S1793557116500649 10.1016/j.amc.2012.09.059 10.1016/j.amc.2003.09.017 10.1016/j.amc.2014.05.074 10.12785/amis/070609 10.1186/s13662-018-1656-1 |
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| SubjectTerms | Appell’s functions confluent hypergeometric function Decomposition Derivatives Fractional calculus Gauss hypergeometric function generating functions Hypergeometric functions incomplete fractional calculus Integrals Mathematics Operators (mathematics) Riemann-Liouville fractional integral |
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