Some Incomplete Hypergeometric Functions and Incomplete Riemann-Liouville Fractional Integral Operators

Mehmet Ali Özarslan and Ceren Ustaoğlu
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Mehmet Ali Özarslan: Department of Mathematics, Faculty of Arts and Sciences, Eastern Mediterranean University, Famagusta, TRNC, Mersin 10, Turkey
Ceren Ustaoğlu: Department of Computer Engineering, Final International University, Toroslar Caddesi, No. 6, Çatalköy, Girne, TRNC, Mersin 10, Turkey

Mathematics, 2019, vol. 7, issue 5, 1-18

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.

Keywords: Gauss hypergeometric function; confluent hypergeometric function; Appell’s functions; incomplete fractional calculus; Riemann-Liouville fractional integral; generating functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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