ON A PARTICULAR CLASS OF MEIJER'S G FUNCTIONS
APPEARING IN FRACTIONAL CALCULUS
D.B. Karp1, J.L. López2
1Far Eastern Federal University
8 Sukhanova St., Vladivostok, 690950, RUSSIA
2Institute of Applied Mathematics, FEBRAS
7 Radio St., Vladivostok, 690041, RUSSIA
2Dpto. de Estadıstica, Informática y Matemáticas
Universidad Pública de Navarra and INAMAT
Campus de Arrosadía, 31006 Pamplona, Navarra, SPAIN

Abstract

In this paper we investigate the Meijer $G$-function $G^{p,1}_{p+1,p+1}$ which, for certain parameter values, represents the Riemann-Liouville fractional integral of the Meijer-Nørlund function $G^{p,0}_{p,p}$. The properties of this function play an important role in extending the multiple Erdélyi-Kober fractional integral operator to arbitrary values of the parameters which is investigated in a separate work, in Fract. Calc. Appl. Anal., Vol. 21, No 5 (2018). Our results for $G^{p,1}_{p+1,p+1}$ include: a regularization formula for overlapping poles, a connection formula with the Meijer-Nørlund function, asymptotic formulas around the origin and unity, formulas for the moments, a hypergeometric transform and a sign stabilization theorem for growing parameters.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 31
Issue: 5
Year: 2018

DOI: 10.12732/ijam.v31i5.1

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