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.

## 1 Answer

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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.