Computation of Fourier transform representations involving the generalized Bessel matrix polynomials

Motivated by the recent studies and developments of the integral transforms with various special matrix functions, including the matrix orthogonal polynomials as kernels, in this article we derive the formulas for Fourier cosine and sine transforms of matrix functions involving generalized Bessel matrix polynomials. With the help of these transforms several results are obtained, which are extensions of the corresponding results in the standard cases. The results given here are of general character and can yield a number of (known and new) results in modern integral transforms.

Automated summary

This article investigates the Fourier cosine and sine transforms of matrix functions involving generalized Bessel matrix polynomials, deriving formulas and obtaining results that extend existing ones. The results presented are of general nature and have implications for various results in modern integral transforms.