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Öğe On generalized two-index hermite matrix polynomials(Univ Miskolc Inst Math, 2017) Kargın, Levent; Kurt, VeliIn this study, we give a new generalization for Hermite matrix polynomials. We obtain some formulas related to an explicit representation, matrix recurrence relations and the Rodrigues formula for two-index Hermite matrix polynomials. Also we generalize Runge's addition formula and Nielsen's identity for these new generalizations. Moreover we give Burchnall's operational formula and Nielsen's identity for Hermite matrix polynomials by means of two-index Hermite matrix polynomials.Öğe Riemann zeta matrix function(Gazi Univ, 2015) Kargın, Levent; Kurt, VeliIn this study, obtaining the matrix analog of the Euler's reflection formula for the classical gamma function we expand the domain of the gamma matrix function and give a infinite product expansion of sin pi xP. Furthermore we define Riemann zeta matrix function and evaluate some other matrix integrals. We prove a functional equation for Riemann zeta matrix function.