Related papers: Higher order Thorin-Bernstein Functions
We generalize generating functions for hypergeometric orthogonal polynomials, namely Jacobi, Gegenbauer, Laguerre, and Wilson polynomials. These generalizations of generating functions are accomplished through series rearrangement using…
One may consider the generalization of Jacobi polynomials and the Jacobi function of the second kind to a general function where the index is allowed to be a complex number instead of a non-negative integer. These functions are referred to…
We construct higher order spectral shift functions, extending the perturbation theory results of M. G. Krein and L. S. Koplienko on representations for the remainders of the first and second order Taylor-type approximations of operator…
We generalize the known constructions of A-hypergeometric functions. In particular, we show that periods of middle dimension on affine or projective complex algebraic varieties are A-hypergeometric functions of coefficients of polynomial…
Matrix elements in different representations are connected by quadratic relations. If matrix elements are those of a $\textit{group element}$, i.e. satisfying the property $\Delta(X) = X\otimes X$, then their generating functions obey…
In a recent paper we introduced sine functions on commutative hypergroups. These functions are natural generalizations of those functions on groups which are products of additive and multiplicative homomorphisms. In this paper we describe…
We examine the power-series solutions and the series solutions in terms of the Hermite functions for the biconfluent Heun equation. Infinitely many cases for which a solution of the biconfluent equation is presented as an irreducible linear…
The real and complex zeros of some special entire functions such as Wright, hyper-Bessel, and a special case of generalized hypergeometric functions are studied by using some classical results of Laguerre, Obreschkhoff, P\'olya and Runckel.…
Inspired by certain interesting recent extensions of the gamma, beta and hypergeometric matrix functions, we introduce here new extension of the gamma and beta matrix function. We also introduce new extensions of the Gauss hypergeometric…
We present the fermionic representation for the q-deformed hypergeometric functions related to Schur polynomials considered by S.Milne \cite{Milne}. For $q=1$ these functions are also known as hypergeometric functions of matrix argument…
Starting from special near-bent functions in dimension 2t-1 we construct bent functions in dimension 2t having a specific derivative. We deduce new famillies of bent functions
Starting from equations obeyed by functions involving the first or the second derivatives of the biconfluent Heun function, we construct two expansions of the solutions of the biconfluent Heun equation in terms of incomplete Beta functions.…
By using Cauchy integral formula in the theory of complex functions, the authors establish some integral representations for the principal branches of several complex functions involving the logarithmic function, find some properties, such…
We review some results of applying the higher covariant derivative regularization to the investigation of quantum corrections structure in N=1 supersymmetric theories. In particular, we demonstrate that all integrals, defining the…
The theory of Selberg zeta functions is generalized to higher rank spaces. Applications towards analytic torsion numbers are given.
Inspired by a recent work of Mesnager, we present several new infinite families of quadratic ternary bent, near-bent and 2-plateaued functions from some known quadratic ternary bent functions. Meanwhile, the distribution of the Walsh…
In the paper, the authors show that the weighted geometric mean and the logarithmic mean are Bernstein functions and establish integral representations of these means by Cauchy's integral theorem in the theory of complex functions.
We consider the equations, arising as the conformal invariance conditions of the perturbed curved beta-gamma system. These equations have the physical meaning of Einstein equations with a B-field and a dilaton on a hermitian manifold, where…
Using a probabilistic approach, we derive several interesting identities involving beta functions. Our results generalize certain well-known combinatorial identities involving binomial coefficients and gamma functions.
We introduce and study the Steiner entire function, an analytic generating function for the intrinsic volumes of a convex compact set in a Hilbert space. This function extends the classical Steiner polynomial to infinite dimensions and…