Abstract
In the present article, we introduce the second Kummer function with matrix parameters and examine its asymptotic behaviour relying on the residue theorem. Further, we provide a closed form of a solution of a Weber matrix differential equation and give a representation using the second Kummer function.
Highlights
We introduce the second Kummer function with matrix parameters and examine its asymptotic behaviour relying on the residue theorem
The application of special functions can be found in theoretical physics [1], probability theory [1, 2], or numerical mathematics [1]
We focus on the asymptotic behaviour of the second Kummer function with matrix parameters
Summary
The application of special functions can be found in theoretical physics [1], probability theory [1, 2], or numerical mathematics [1]. The main goal of this article is to introduce the second Kummer function with matrix parameters and to study its asymptotic behaviour. This function appears as a solution of an equation in mathematical finance, where a Markovian regime switching framework (see [8, 9] as an example) is combined with an equilibrium model for asset bubbles from [10, 11]. It contains the definition of the second Kummer function, with matrix parameters L and bI and a complex argument z, as. The representation of this solution uses parabolic cylinder functions with matrix parameters
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