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Title: Fractional Extensions of Jacobi Polynomials and Gauss Hypergeometric Function
Authors: Gogovcheva, Elena
Boyadjiev, Lyubomir
Keywords: Riemann–Liouville Fractional Differentiation and Integration Operators
Jacobi Polynomials
Rodrigues' Representation
Fractional Jacobi Functions
Gauss Hypergeometric Differential Equation
Fractional Gauss Functions
Issue Date: 2005
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Fractional Calculus and Applied Analysis, Vol. 8, No 4, (2005), 431p-438p
Abstract: This paper refers to a fractional order generalization of the classical Jacobi polynomials. Rodrigues’ type representation formula of fractional order is considered. By means of the Riemann–Liouville operator of fractional calculus fractional Jacobi functions are defined, some of their properties are given and compared with the corresponding properties of the classical Jacobi polynomials. These functions appear as a special case of a fractional Gauss function, defined as a solution of the fractional generalization of the Gauss hypergeometric equation.
Description: 2000 Mathematics Subject Classification: 26A33, 33C45
ISSN: 1311-0454
Appears in Collections:2005

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