The Multıvarıable Hypergeometrıc Functıons

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Thesis Type: Doctorate

Institution Of The Thesis: Gazi University, Fen Bilimleri Enstitüsü, Turkey

Approval Date: 2017

Thesis Language: Turkish

Student: DÜRİYE KORKMAZ DÜZGÜN

Supervisor: Esra Erkus-Duman

Open Archive Collection: AVESIS Open Access Collection

Abstract:

This thesis is based on extended multivariable hypergeometric functions. Firstly, the classes of bilinear generating functions for extended second kind Appell functions are obtained. By defining extended fourth kind Horn functions containing one parameter, some generating functions and bilateral generating function relations for these functions are given. Furthermore, extended multivariable fourth kind Horn functions containing two parameters are defined, and then families of generating and bilateral generating functions are obtained for these functions. Finally, multilinear and multilateral generating function relations for extended multivariable fourth kind Horn functions are derived, and also some special cases between these functions and other polynomials are discussed.