Related papers: Construction of the Digamma Function by Derivative…
The structure functions of the Lagrangian gauge algebra are given explicitly in terms of the hamiltonian constraints and the first order Hamiltonian structure functions and their derivatives.
We show how certain hypergeometric functions play an important role in finding fundamental solutions for a generalized Tricomi operator.
We study orthogonal polynomials for a weight function defined over a domain of revolution, where the domain is formed from rotating a two-dimensional region and goes beyond the quadratic domains. Explicit constructions of orthogonal bases…
The purpose of these notes is to give a short survey of an interesting connection between partition functions of supersymmetric gauge theories and hypergeometric functions and to present the recent progress in this direction.
The aim of this paper is to exhibit a method for proving that certain analytic functions are not solutions of algebraic differential equations. The method is based on model-theoretic properties of differential fields and properties of…
Dimensional analysis provides many simple and useful tools for various situations in science. The objective of this paper is to investigate its relations to functions, i.e., the dimensions for functions that yield physical quantities and…
This report (written in French) is devoted to studying special functions the most used in physics. Special functions are a very broad branch of mathematics, theoretical physics, and mathematical physics. They appeared in the nineteenth…
Superconformal methods are useful to build invariant actions in supergravity. We have a good insight in the possibilities of actions that are at most quadratic in spacetime derivatives, but insight in general higher-derivative actions is…
We show some of the mathematics that is being developed for the computation of deep inelastic structure functions to three loops. These include harmonic sums, harmonic polylogarithms and a class of difference equations that can be solved…
This paper presents an algebraic-geometric construction of the derivative developed initially within the class of polynomial functions without introducing limits at the initial stage. Tangency is characterized by an algebraic condition: the…
Functionals (i.e. functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the…
The definite integral with the kernel x/(x^2+b^2)/[\exp(2\pi x)-1] integrated from x=0 to infinity is the main term of a representation of the Digamma-Function psi(b), the derivative of the logarithm of the Gamma-Function. We present…
The relationship between Feynman diagrams and hypergeometric functions is discussed. Special attention is devoted to existing techniques for the construction of the $\epsilon$-expansion. As an example, we present a detailed discussion of…
The field of meromorphic functions on a sigma divisor of a hyperelliptic curve of genus $3$ is described in terms of the gradient of it's sigma function. Solutions of corresponding families of polynomial dynamical systems in $\mathbb{C}^4$…
We consider the set of power functions defined on the set of positive real number, and their linear combinations. After recalling some properties of the gamma function, we give two general definitions of derivatives of positive and negative…
Motivated by string theory connection, a covariant procedure for perturbative calculation of the partition function of the two-dimensional generalized $\sigma$-model is considered. The importance of a consistent regularization of the…
A function is differentially algebraic (or simply D-algebraic) if there is a polynomial relationship between some of its derivatives and the indeterminate variable. Many functions in the sciences, such as Mathieu functions, the Weierstrass…
The derivative polynomials for the hyperbolic and trigonometric tangent, cotangent and secant are found in explicit form, where the coefficients are given in terms of Stirling numbers of the second kind. As application, some integrals are…
Derivative-matching approximations are constructed as power series built from functions. The method assumes the knowledge of special values of the Bell polynomials of the second kind, for which we refer to the literature. The presented…
Multifractals are inhomogeneous measures (or functions) which are typically described by a full spectrum of real dimensions, as opposed to a single real dimension. Results from the study of fractal strings in the analysis of their geometry,…