Fractional Extensions of Jacobi Polynomials and Gauss Hypergeometric Function
| Data(s) |
28/08/2010
28/08/2010
2005
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| Resumo |
2000 Mathematics Subject Classification: 26A33, 33C45 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. * Partially supported by Project MM 1305 - National Science Fund, Bulgarian Ministry of Educ. Sci. |
| Identificador |
Fractional Calculus and Applied Analysis, Vol. 8, No 4, (2005), 431p-438p 1311-0454 |
| Idioma(s) |
en |
| Publicador |
Institute of Mathematics and Informatics Bulgarian Academy of Sciences |
| Palavras-Chave | #Riemann–Liouville Fractional Differentiation and Integration Operators #Jacobi Polynomials #Rodrigues' Representation #Fractional Jacobi Functions #Gauss Hypergeometric Differential Equation #Fractional Gauss Functions #26A33 #33C45 |
| Tipo |
Article |
