The representation of this solution uses parabolic cylinder functions with matrix parameters.
The Weber matrix differential equation provides us with an example for the use of parabolic cylinder functions with matrix parameters.
Moreover, we introduce the parabolic cylinder function with matrix parameters in the present article and analyse its asymptotic behaviour.
(43) are pertained to the type of ordinary differential equations for the parabolic cylinder functions. However, it is necessary to rearrange their form to a canonical one (see ) which looks as
They are expressible via products of the parabolic cylinder functions (47).