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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Bibliographic Details
Published in:Mathematics (Basel) Vol. 7; no. 5; p. 483
Main Authors: Özarslan, Mehmet Ali, Ustaoğlu, Ceren
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.05.2019
Subjects:
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
ISSN:2227-7390, 2227-7390
Online Access:Get full text
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Summary: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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ISSN:2227-7390
2227-7390
DOI:10.3390/math7050483