IncGamma {HypergeoMat}

Incomplete Gamma function of a matrix argument

Description

Evaluates the incomplete Gamma function of a matrix argument.

Usage

IncGamma(m, a, x)

Arguments

m

truncation weight of the summation, a positive integer

a

real or complex parameter with Re(a)>(p-1)/2, where p is the dimension (the order of the matrix)

x

either a real or complex square matrix, or a numeric or complex vector, the eigenvalues of the matrix

Value

A real or complex number.

Note

This function is usually defined for a symmetric real matrix or a Hermitian complex matrix.

References

A. K. Gupta and D. K. Nagar. Matrix variate distributions. Chapman and Hall, 1999.

Examples

# for a scalar x, this is the incomplete Gamma function:
a <- 2
x <- 1.5
IncGamma(m = 15, a, x)
gsl::gamma_inc_P(a, x)
pgamma(x, shape = a, rate = 1)