Related papers: Solving conformable Gegenbauer differential equati…
The aim of the present paper is to study the regularity properties of the solution of a backward stochastic differential equation with a monotone generator in infinite dimension. We show some applications to the nonlinear Kolmogorov…
In this paper we have studied the most general generating function of reduction for one loop integrals with arbitrary tensor structure in numerator and arbitrary power distribution of propagators in denominator. Using IBP relations, we have…
This paper deals with the series solution of a linear delay differential equation (DDE) y'(x) = ay(x)+ by(q x), 0<q<1 with proportional delay. We discuss the convergence of this novel series. We establish the relation between the special…
We present a general formula for the particular solution of an inhomogeneous linear difference equation with variable coefficients. The answer is expressed as a weighted sum of fundamental solutions of the associated linear difference…
The coefficients of certain operators on $V\otimes V$ can be constructed using generating functions. Necessary and sufficient conditions are given for some such operators to satisfy the Yang-Baxter equation. As a corollary we obtain a…
In this paper we show how to find a closed form solution for third order difference operators in terms of solutions of second order operators. This work is an extension of previous results on finding closed form solutions of recurrence…
We derive the Cardano formula of cubic equations by completing the cube, and provide radical solutions to some algebraic equations of higher degree by completing powers. The main idea of completing powers arises from Harrison's center…
We find the Hecke-Rogers type series representations of generating functions of the Hurwitz class numbers which is very close to certain mock theta functions. We also prove two combinatorial interpretation of Hurwitz class numbers appeared…
In this paper, we discuss sums of powers of the positive integers and compute both the exponential and ordinary generating functions for these sums. We express these generating functions in terms of exponential and geometric polynomials and…
The purpose of this article is to analyze the connection between Eynard-Orantin topological recursion and formal WKB solutions of a $\hbar$-difference equation: $\Psi(x+\hbar)=\left(e^{\hbar\frac{d}{dx}}\right) \Psi(x)=L(x;\hbar)\Psi(x)$…
We define a generalization of convex functions, which we call $\delta$-convex functions, and show they must satisfy interior H\"older and $W^{1,p}$ estimates. As an application, we consider solutions of a certain class of fully nonlinear…
We study compositions of a positive integer $n$ in which the occurrence of even parts larger than a fixed threshold $k$ is controlled. More precisely, for each composition $m=(m_1,\dots,m_r)$ we consider the number of even parts strictly…
Consider an ordinary generating function $\sum_{k=0}^{\infty}c_kx^k$, of an integer sequence of some combinatorial relevance, and assume that it admits a closed form $C(x)$. Various instances are known where the corresponding truncated sum…
In this paper we present a generating function approach to two counting problems in elementary quantum mechanics. The first is to find the total ways of distributing identical particles among different states. The second is to find the…
In the paper, by a general and fundamental, but non-extensively circulated, formula for derivatives of a ratio of two differentiable functions and by a recursive relation of the Hessenberg determinant, the author finds a new determinantal…
The main result of the article says that the formal power series equal to the ratio of two neighboring Chebyshev polynomials, after some renormalization, approximates the generating function of the Catalan numbers. We present a proof of…
We prove that every countable group with solvable power problem embeds into a finitely presented 2-generated group with solvable power and conjugacy problems.
Given a first-order autonomous algebraic ordinary differential equation, we present a method for computing formal power series solutions by means of places. We provide an algorithm for computing a full characterization of possible initial…
The method of generating functional is generalized to the case of strongly correlated systems, and applied to the Hubbard model. For the electronic Green's function constructed for Hubbard operators, an equation using variational…
The aim of this paper is to study generating functions for the coefficients of the classical superoscillatory function associated with weak measurements. We also establish some new relations between the superoscillatory coefficients and…