On the hypergeometric matrix function
نویسندگان
چکیده
منابع مشابه
A Hypergeometric Function Transform and Matrix-valued Orthogonal Polynomials
The spectral decomposition for an explicit second-order differential operator T is determined. The spectrum consists of a continuous part with multiplicity two, a continuous part with multiplicity one, and a finite discrete part with multiplicity one. The spectral analysis gives rise to a generalized Fourier transform with an explicit hypergeometric function as a kernel. Using Jacobi polynomial...
متن کاملThe matrix-valued hypergeometric equation.
The hypergeometric differential equation was found by Euler [Euler, L. (1769) Opera Omnia Ser. 1, 11-13] and was extensively studied by Gauss [Gauss, C. F. (1812) Comm. Soc. Reg. Sci. II 3, 123-162], Kummer [Kummer, E. J. (1836) Riene Ang. Math. 15, 39-83; Kummer, E. J. (1836) Riene Ang. Math. 15, 127-172], and Riemann [Riemann, B. (1857) K. Gess. Wiss. 7, 1-24]. The hypergeometric function kno...
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The special case of the hypergeometric function 2F1 represents the binomial series (1 + x) = ∑∞ n=0 ( α n ) xn that always converges when |x| < 1. Convergence of the series at the endpoints, x = ±1, depends on the values of α and needs to be checked in every concrete case. In this note, using new approach, we reprove the convergence of the hypergeometric series for |x| < 1 and obtain new result...
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We consider representations of quadratic R-matrix algebras by means of certain first order ordinary differential operators. These operators turn out to act as parameter shifting operators on the Gauss hypergeometric function and its limit cases and on classical orthogonal polynomials. The relationship with W. Miller’s treatment of Lie algebras of first order differential operators will be discu...
متن کاملThe Generalized Matrix Valued Hypergeometric Equation
Abstract. The matrix valued analog of the Euler’s hypergeometric differential equation was introduced by Tirao in [1]. This equation arises in the study of matrix valued spherical functions and in the theory of matrix valued orthogonal polynomials. The goal of this paper is to extend naturally the number of parameters of Tirao’s equation in order to get a generalized matrix valued hypergeometri...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1998
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(98)00158-7