BesselA {HypergeoMat}

Type one Bessel function of Herz

Description

Evaluates the type one Bessel function of Herz.

Usage

BesselA(m, x, nu)

Arguments

m

truncation weight of the summation, a positive integer

x

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

nu

the order parameter, real or complex number with Re(nu)>-1

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, the relation with the Bessel J-function:
t <- 2
nu <- 3
besselJ(t, nu)
BesselA(m=15, t^2/4, nu) * (t/2)^nu
# it also holds for a complex variable:
if(require("Bessel")) {
  t <- 1 + 2i
  Bessel::BesselJ(t, nu)
  BesselA(m=15, t^2/4, nu) * (t/2)^nu
}