# Fractional Extensions of Jacobi Polynomials and Gauss Hypergeometric Function

Gogovcheva, Elena; Boyadjiev, Lyubomir

Fractional Calculus and Applied Analysis (2005)

- Volume: 8, Issue: 4, page 431-438
- ISSN: 1311-0454

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topGogovcheva, 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 -

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