BesselA: Type one Bessel function of Herz

In stla/HypergeoMatEigen: Hypergeometric Function of a Matrix Argument

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:
t <- 1 + 2i
Bessel::BesselJ(t, nu)
BesselA(m=15, t^2/4, nu) * (t/2)^nu

stla/HypergeoMatEigen documentation built on Jan. 30, 2022, 12:36 a.m.