A class of infinite series including terms of generalized sequences.
A Levy-Khinchin Formula for Semigroups with Involutions.
A proof of a conjecture by Karamata.
A proof of Leibniz's formula for divided differences.
Addendum to the article: Polylogarithms in the field of omega (a root of a given cubic): Functional equations and ladders.
An Apéry-like difference equation for Catalan's constant.
Analog of Favard's Theorem for Polynomials Connected with Difference Equation of 4-th Order
Orthonormal polynomials on the real line {pn (λ)} n=0 ... ∞ satisfy the recurrent relation of the form: λn−1 pn−1 (λ) + αn pn (λ) + λn pn+1 (λ) = λpn (λ), n = 0, 1, 2, . . . , where λn > 0, αn ∈ R, n = 0, 1, . . . ; λ−1 = p−1 = 0, λ ∈ C. In this paper we study systems of polynomials {pn (λ)} n=0 ... ∞ which satisfy the equation: αn−2 pn−2 (λ) + βn−1 pn−1 (λ) + γn pn (λ) + βn pn+1 (λ) + αn pn+2 (λ) = λ2 pn (λ), n = 0, 1, 2, . . . , where αn > 0, βn ∈ C, γn ∈ R, n = 0, 1, 2, . . ., α−1 = α−2...
Asymptotical behaviors of nonautonomous discrete Kolmogorov system with time lags.