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Low-rank tensor representation of Slater-type and Hydrogen-like orbitals

Martin Mrovec (2017)

Applications of Mathematics

The paper focuses on a low-rank tensor structured representation of Slater-type and Hydrogen-like orbital basis functions that can be used in electronic structure calculations. Standard packages use the Gaussian-type basis functions which allow us to analytically evaluate the necessary integrals. Slater-type and Hydrogen-like orbital functions are physically more appropriate, but they are not analytically integrable. A numerical integration is too expensive when using the standard discretization...

Matrix valued orthogonal polynomials of Jacobi type: the role of group representation theory

F. Alberto Grünbaum, Inés Pacharoni, Juan Alfredo Tirao (2005)

Annales de l’institut Fourier

The main purpose of this paper is to present new families of Jacobi type matrix valued orthogonal polynomials obtained from the underlying group S U ( n ) and its representations. These polynomials are eigenfunctions of some symmetric second order hypergeometric differential operator with matrix coefficients. The final result holds for arbitrary values of the parameters α , β > - 1 , but it is derived only for those values that come from the group theoretical setup.

Matrix-Variate Statistical Distributions and Fractional Calculus

Mathai, A., Haubold, H. (2011)

Fractional Calculus and Applied Analysis

MSC 2010: 15A15, 15A52, 33C60, 33E12, 44A20, 62E15 Dedicated to Professor R. Gorenflo on the occasion of his 80th birthdayA connection between fractional calculus and statistical distribution theory has been established by the authors recently. Some extensions of the results to matrix-variate functions were also considered. In the present article, more results on matrix-variate statistical densities and their connections to fractional calculus will be established. When considering solutions of fractional...

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