On Tricomi and Hermite-Tricomi matrix functions of complex variable.(English)Zbl 1266.33012

Summary: Tricomi and Hermite-Tricomi matrix functions are introduced starting from the Hermite matrix polynomials. The convergence, radius of regularity, integral form, generating matrix functions, matrix recurrence relations satisfied by these Tricomi matrix functions are derived. Finally, the generating matrix functions, matrix recurrence relations, addition theorems for the Hermite-Tricomi matrix functions are given and matrix differential equations satisfied by them are presented.

MSC:

 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) 15A16 Matrix exponential and similar functions of matrices 33C05 Classical hypergeometric functions, $${}_2F_1$$