Reference request for Bessel function of the second kind with matrix argument

Question

As the title says, I would like to know if anyone could provide a reference which provides the definition and properties of the Bessel function of the second kind with matrix argument. If possible, I would appreciate as well any reference which provides its power series.

Answer 1

Because Bessel functions of the first and second kind are related by $$Y_\nu(z)=\frac{J_\nu(z)\cos\pi\nu-J_{-\nu}(z)}{\sin \pi\nu},$$ you can refer to literature that studies the function $J_\nu$ with matrix argument:

• Bessel Functions of Matrix Argument (1955)
• Laplace approximation for Bessel functions of matrix argument (2003)

Section 7 of the 1955 paper gives the power series.