On a Particular Class of Meijer's G Functions Appearing in Fractional Calculus

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.