Related papers: Some Partial Fraction Identities associated with t…
Functional iterations such as Newton's are a popular tool for polynomial root-finding. We consider realistic situation where some (e.g., better-conditioned) roots have already been approximated and where further computations is directed to…
These notes are an expanded version of a talk given by the second author. Our main interest is focused on the challenging problem of computing Kronecker coefficients. We decided, at the beginning, to take a very general approach to the…
We describe a simple method that produces automatically closed forms for the coefficients of continued fractions expansions of a large number of special functions. The function is specified by a non-linear differential equation and initial…
Motivated by the fact that the classical Jacobi theta function $\vartheta$ is the exponential generating function of the Eisenstein series, we study the exponential Taylor coefficients (in the elliptic variable) of a related natural partial…
We investigate the possibilities to calculate vector partition functions by means of iterated partial fraction decomposition, as suggested by Beck (2004). Particularly, for an important type of families of rational functions, we describe an…
After obtaining some useful identities, we prove an additional functional relation for $q$ exponentials with reversed order of multiplication, as well as the well known direct one in a completely rigorous manner.
Quaternionic analysis relies heavily on results on functions defined on domains in $\mathbb R^4$ (or $\mathbb R^3$) with values in $\mathbb H$. This theory is centered around the concept of $\psi-$hyperholomorphic functions i.e.,…
Our overall goal is to unify and extend some results in the literature related to the approximation of generating functions of finite and infinite sequences over a field by rational functions. In our approach, numerators play a significant…
We introduce a $q$-analog of the higher continued fractions introduced by the last three authors in a previous work (together with Gregg Musiker), which are simultaneously a generalization of the $q$-rational numbers of Morier-Genoud and…
We give a new proof for a theorem of Ehrhart regarding the quasi-polynomiality of the function that counts the number of integer points in the integral dilates of a rational polytope. The proof involves a geometric bijection,…
Using basic hypergeometric functions and partial fraction decomposition we give a new kind of generalization of identities due to Uchimura, Dilcher, Van Hamme, Prodinger, and Chen-Fu related to divisor functions. An identity relating…
Recently, Guo and Sun derived an identity for factorial Grothendieck polynomials which is a generalization of the one for Schur polynomials by Feh\'er, N\'emethi and Rim\'anyi. We analyze the identity from the point of view of quantum…
We introduce a class of integral theorems based on cyclic functions and Riemann sums approximating integrals. The Fourier integral theorem, derived as a combination of a transform and inverse transform, arises as a special case. The…
In the present paper, by extending some fractional calculus to the framework of Cliffors analysis, new classes of wavelet functions are presented. Firstly, some classes of monogenic polynomials are provided based on 2-parameters weight…
A novel representation is developed as a measure for multilinear fractional embedding. Corresponding extensions are given for the Bourgain-Brezis-Mironescu theorem and Pitt's inequality. New results are obtained for diagonal trace…
Andrews and Keith recently produced a general Schmidt type partition theorem using a novel interpretation of Stockhofe's bijection, which they used to find new $q$-series identities. This includes an identity for a trivariate 2-colored…
The results presented in this paper are refinements of some results presented in a previous paper. Three such refined results are presented. The first one relaxes one of the basic hypotheses assumed in the previous paper, and thus extends…
Product identities in two variables $x, q$ expand infinite products as infinite sums, which are linear combinations of theta functions; famous examples include Jacobi's triple product identity, Watson's quintuple identity, and Hirschhorn's…
We analyze and test using Fourier extensions that minimize a Hilbert space norm for the purpose of solving partial differential equations (PDEs) on surfaces. In particular, we prove that the approach is arbitrarily high-order and also show…
We present a deformed algebra related to the q-exponential and the q-logarithm functions that emerge from nonextensive statistical mechanics. We also develop a q-derivative (and consistently a q-integral) for which the q-exponential is an…