Abstract
In this paper, we consider a Humbert matrix function in the following form:
J(A,B)(z) = (z/3)(A+B) Gamma(-1)(A + I)Gamma(-1)(B + I) F-0(2)(-,-; A + I, B + I; -z(3)/27), vertical bar z vertical bar < infinity,
where
F-0(2) (-, -; A + I, B + I; -z(3)/27)( )=( )Gamma(A + I)Gamma(B+I) x Sigma(infinity)(k=0) (-1)(k)Gamma(-1)(A+ (k + 1)I)Gamma(-1)(B + (k + 1)I/k! x (z/3)(3k), ( )
and for this function we present order and type, integral representations and differential recurrence relations.