Some properties of Gamma and Beta matrix functions

RETRACTED: On Humbert matrix functions

“…The gamma matrix function C(P) and the beta matrix function B(P, Q) have been defined in [9], as follows Let P and Q be commuting matrices in C NÂN such that the matrices P + nI, Q + nI and P + Q + nI are invertible for every integer n P 0. Then according to [9], we have BðP; QÞ ¼ CðPÞCðQÞ½CðP þ QÞ À1 : ð1:9Þ…”

Tauberian theorems for matrix regular variation

“…That Γ( P ) and P commute follows directly from (3.3). Finally, it follows from [9] that Γ( P ) is invertible.…”

Lie algebra and Laguerre Matrix Polynomials of One Variable

“…From [5] if A + nI is an invertible matrix for all integers n ≥ 0 then the matrix version of the Pochhammer symbol is…”