Related papers: The Lemniscatic Functions
We derive new approximate representations of the Lommel functions in terms of the Scorer function and approximate representations of the first derivative of the Lommel functions in terms of the derivative of the Scorer function. Using the…
Cyclotomic polylogarithms are reviewed and new results concerning the special constants that occur are presented. This also allows some comments on previous literature results using PSLQ.
In this work we develop a theory of Stieltjes-analytic functions. We first define the Stieltjes monomials and polynomials and we study them exhaustively. Then, we introduce the Stieltjes analytic functions locally, as an infinite series of…
The thesis gave a fine study on the distribution of the coefficients of automorphic L-functions for GL(m) with m>1. In particular we have treated two types of problems: change of signs of these coefficients (when they are real) and their…
This is the first installment in a series of papers devoted to examining certain aspects of the asymptotic value distribution and distribution of zeros manifested by members of a broad class of linear combinations of L-functions in the…
In this paper, we continue studying the properties of $\gamma$-semi-continuous and $\gamma$-semi-open functions introduced in [5].
In this paper, we study the Lagrangian functions for a class of second-order differential systems arising from physics. For such systems, we present necessary and sufficient conditions for the existence of Lagrangian functions. Based on the…
We define the functional LYZ ellipsoid of log-concave functions. Then we give notes appended to [6].
Plethysm of two Schur functions can be expressed as a linear combination of Schur functions, and monomial symmetric functions. In this paper, we express the coefficients combinatorially in the case of monomial symmetric functions. And by…
Starting from a recent result expressing the Lerch zeta function as a fractional derivative, we consider further fractional derivatives of the Lerch zeta function with respect to different variables. We establish a partial differential…
In this course of lectures we give an account of the growth theory of subharmonic functions, which is directed towards its applications to entire functions of one and several complex variables.
Let L be a bounded distributive lattice. We give several characterizations of those L^n --> L mappings that are polynomial functions, i.e., functions which can be obtained from projections and constant functions using binary joins and…
The general properties of two-dimensional generalized Bessel functions are discussed. Various asymptotic approximations are derived and applied to analyze the basic structure of the two-dimensional Bessel functions as well as their nodal…
We introduce the notion of orbital L-functions for the space of binary cubic forms and investigate their analytic properties. We study their functional equations and residue formulas in some detail. Aside from the intrinsic interest,…
We formulate some problems and conjectures about semigroups of rational functions under composition. The considered problems arise in different contexts, but most of them are united by a certain relationship to the concept of amenability.
We study the correlation functions of logarithmic conformal field theories. First, assuming conformal invariance, we explicitly calculate two-- and three-- point functions. This calculation is done for the general case of more than one…
We obtain classical solutions of $\l$-deformed $\s$-models based on $SL(2,\mathbb{R})/U(1)$ and $SU(2)/U(1)$ coset manifolds. Using two different sets of coordinates, we derive two distinct classes of solutions. The first class is expressed…
Special values of the Lommel functions allow the calculation of Fresnel like integrals. These closed form expressions along with their asymptotic values are reported.
This is the first part of the review article which focuses on theory and applications of Herglotz-Nevanlinna functions in material sciences. It starts with the definition of scalar valued Herglotz-Nevanlinna functions and explains in detail…
The aim of this paper is to put the fundations of a new theory of functions, called holomorphic Cliffordian, which should play an essential role in the generalization of holomorphic functions to higher dimensions. Let R\_{0,2m+1} be the…