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35 Functions of Matrix ArgumentProperties

§35.3 Multivariate Gamma and Beta Functions

Contents
  1. §35.3(i) Definitions
  2. §35.3(ii) Properties

§35.3(i) Definitions

35.3.3 Bm(a,b)=0<X<I|X|a12(m+1)|IX|b12(m+1)dX,
(a),(b)>12(m1).

§35.3(ii) Properties

35.3.4 Γm(a)=πm(m1)/4j=1mΓ(a12(j1)).
35.3.5 Γm(s1,,sm)=πm(m1)/4j=1mΓ(sj12(j1)).
35.3.6 Γm(a,,a)=Γm(a).
35.3.7 Bm(a,b)=Γm(a)Γm(b)Γm(a+b).
35.3.8 Bm(a,b)=Ω|X|a12(m+1)|I+X|(a+b)dX,
(a),(b)>12(m1).