Fractional Extensions of Jacobi Polynomials and Gauss Hypergeometric Function

Gogovcheva, Elena, and Boyadjiev, Lyubomir. "Fractional Extensions of Jacobi Polynomials and Gauss Hypergeometric Function." Fractional Calculus and Applied Analysis 8.4 (2005): 431-438. <http://eudml.org/doc/11252>.

@article{Gogovcheva2005,
abstract = {2000 Mathematics Subject Classification: 26A33, 33C45This 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.},
author = {Gogovcheva, Elena, Boyadjiev, Lyubomir},
journal = {Fractional Calculus and Applied Analysis},
keywords = {26A33; 33C45},
language = {eng},
number = {4},
pages = {431-438},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Fractional Extensions of Jacobi Polynomials and Gauss Hypergeometric Function},
url = {http://eudml.org/doc/11252},
volume = {8},
year = {2005},
}

TY - JOUR
AU - Gogovcheva, Elena
AU - Boyadjiev, Lyubomir
TI - Fractional Extensions of Jacobi Polynomials and Gauss Hypergeometric Function
JO - Fractional Calculus and Applied Analysis
PY - 2005
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 8
IS - 4
SP - 431
EP - 438
AB - 2000 Mathematics Subject Classification: 26A33, 33C45This 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.
LA - eng
KW - 26A33; 33C45
UR - http://eudml.org/doc/11252
ER -