Infinite sums as linear combinations of polygamma functions
Integer powers of arcsin.
Integral averages of multiple Poisson kernels.
Kashaev's conjecture and the Chern-Simons invariants of knots and links.
Laguerre-type exponentials, and the relevant -circular and -hyperbolic functions.
L'identité de Barnes pour les corps finis
Linear differential equations and multiple zeta values. I. Zeta(2)
Certain generating fuctions for multiple zeta values are expressed as values at some point of solutions of linear meromorphic differential equations. We apply asymptotic expansion methods (like the WKB method and the Stokes operators) to solutions of these equations. In this way we give a new proof of the Euler formula ζ(2) = π²/6. In further papers we plan to apply this method to study some third order hypergeometric equation related to ζ(3).
Logarithmic and antilogarithmic mappings [Book]
Logarithmic derivative of the Euler Γ function in Clifford analysis.
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.
Logarithmus faktorielly
Logarithmy hyperbolické
Low-rank tensor representation of Slater-type and Hydrogen-like orbitals
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 solutions of the functional equation of the gamma function.
Mémoire sur les développements en fractions continues de la fonction exponentielle, pouvant servir d'introduction à la théorie des fractions continues algébriques
Mercerian Theorems Involving Cesàro Means of Positive Order.
Methodické poznámky k odvozování periodičnosti funkce exponenciální
Monotonic and logarithmically convex properties of a function involving gamma functions.
Monotonicity and concavity properties of some functions involving the gamma function with applications.
Monotonicity and convexity for the gamma function.
Monotonicity properties of the relative error of a Padé approximation for Mills' ratio.