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Logarithmic derivative of the Euler Γ function in Clifford analysis.

Guy Laville, Louis Randriamihamison (2005)

Revista Matemática Iberoamericana

The logarithmic derivative of the Γ-function, namely the ψ-function, has numerous applications. We define analogous functions in a four dimensional space. We cut lattices and obtain Clifford-valued functions. These functions are holomorphic cliffordian and have similar properties as the ψ-function. These new functions show links between well-known constants: the Eurler gamma constant and some generalisations, ζR(2), ζR(3). We get also the Riemann zeta function and the Epstein zeta functions.

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...

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