Fractional Integration of the Product of Bessel Functions of the First Kind

Kilbas, Anatoly, and Sebastian, Nicy. "Fractional Integration of the Product of Bessel Functions of the First Kind." Fractional Calculus and Applied Analysis 13.2 (2010): 159-176. <http://eudml.org/doc/219642>.

@article{Kilbas2010,
abstract = {Dedicated to 75th birthday of Prof. A.M. Mathai, Mathematical Subject Classification 2010:26A33, 33C10, 33C20, 33C50, 33C60, 26A09Two integral transforms involving the Gauss-hypergeometric function in the kernels are considered. They generalize the classical Riemann-Liouville and Erdélyi-Kober fractional integral operators. Formulas for compositions of such generalized fractional integrals with the product of Bessel functions of the first kind are proved. Special cases for the product of cosine and sine functions are given. The results are established in terms of generalized Lau-ricella function due to Srivastava and Daoust. Corresponding assertions for the Riemann-Liouville and Erdélyi-Kober fractional integrals are presented.},
author = {Kilbas, Anatoly, Sebastian, Nicy},
journal = {Fractional Calculus and Applied Analysis},
keywords = {Fractional Integrals; Bessel Function of the First Kind; Generalized Hypergeometric Series; Generalized Lauricella Series in Several Variables; Cosine and Sine Trigonometric Functions; fractional integrals; Bessel function of first kind; generalized hypergeometric series; generalized Lauricella series in several variables; cosine and sine trigonometric functions},
language = {eng},
number = {2},
pages = {159-176},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Fractional Integration of the Product of Bessel Functions of the First Kind},
url = {http://eudml.org/doc/219642},
volume = {13},
year = {2010},
}

TY - JOUR
AU - Kilbas, Anatoly
AU - Sebastian, Nicy
TI - Fractional Integration of the Product of Bessel Functions of the First Kind
JO - Fractional Calculus and Applied Analysis
PY - 2010
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 13
IS - 2
SP - 159
EP - 176
AB - Dedicated to 75th birthday of Prof. A.M. Mathai, Mathematical Subject Classification 2010:26A33, 33C10, 33C20, 33C50, 33C60, 26A09Two integral transforms involving the Gauss-hypergeometric function in the kernels are considered. They generalize the classical Riemann-Liouville and Erdélyi-Kober fractional integral operators. Formulas for compositions of such generalized fractional integrals with the product of Bessel functions of the first kind are proved. Special cases for the product of cosine and sine functions are given. The results are established in terms of generalized Lau-ricella function due to Srivastava and Daoust. Corresponding assertions for the Riemann-Liouville and Erdélyi-Kober fractional integrals are presented.
LA - eng
KW - Fractional Integrals; Bessel Function of the First Kind; Generalized Hypergeometric Series; Generalized Lauricella Series in Several Variables; Cosine and Sine Trigonometric Functions; fractional integrals; Bessel function of first kind; generalized hypergeometric series; generalized Lauricella series in several variables; cosine and sine trigonometric functions
UR - http://eudml.org/doc/219642
ER -