相关论文: Perturbative connection formulas for Heun equation…

We introduce a nine-parameter Heun-type differential equation and obtain three classes of its solutions as series of square integrable functions written in terms of the Jacobi polynomial. The expansion coefficients of the series satisfy…

This thesis provides an extension of the work of Dirk Kreimer and Alain Connes on the Hopf algebra structure of Feynman graphs and renormalization to general graphs. Additionally, an algebraic structure of the asymptotics of formal power…

Building on our previous works on perturbative solutions to a Schwinger-Dyson for the massless Wess-Zumino model, we show how to compute 1/n corrections to its asymptotic behavior. The coefficients are analytically determined through a sum…

Several expansions of the solutions to the confluent Heun equation in terms of incomplete Beta functions are constructed. A new type of expansion involving certain combinations of the incomplete Beta functions as expansion functions is…

We consider a self-convolutive recurrence whose solution is the sequence of coefficients in the asymptotic expansion of the logarithmic derivative of the confluent hypergeometic function $U(a,b,z)$. By application of the Hilbert transform…

The method of Frobenius is a standard technique to construct series solutions of an ordinary linear differential equation around a regular singular point. In the classical case, when the roots of the indicial polynomial are separated by an…

The usual fluid equations describing the large-scale evolution of mass density in the universe can be written as local in the density, velocity divergence, and velocity potential fields. As a result, the perturbative expansion in small…

Summation formulae are classical tools in analysis: Taylor-MacLaurin, Euler-MacLaurin, Poisson, Vorono\"i, Circle formulae\ldots We will show how, from a single equation - referred to as the mother-equation - it is possible to unify these…

In this paper we study the Frobenius characters of the invariant subspaces of the tensor powers of a representation V. The main result is a formula for these characters for a polynomial functor of V involving the characters for V. The main…

We find sets of solutions to the generalized spheroidal wave equation (GSWE) or, equivalently, to the confluent Heun equation. Each set is constituted by three solutions, one given by a series of ascending powers of the independent…

A thorough account is given of the derivation of uniform semiclassical approximations to the particle and kinetic energy densities of N noninteracting bounded fermions in one dimension. The employed methodology allows the inclusion of…

We are interested in the long-time asymptotic behavior of growth-fragmentation equations with a nonlinear growth term. We present examples for which we can prove either the convergence to a steady state or conversely the existence of…

We formulate a notion of abstract loop equations, and show that their solution is provided by a topological recursion under some assumptions, in particular the result takes a universal form. The Schwinger-Dyson equation of the one and two…

This is the first of a two-part paper which determines necessary and sufficient conditions on the asymptotic behaviour of forcing functions so that the solutions of additively pertubed linear differential equations obey certain growth or…

Sequences that are defined by multisums of hypergeometric terms with compact support occur frequently in enumeration problems of combinatorics, algebraic geometry and perturbative quantum field theory. The standard recipe to study the…

An expression for the oscillatory part of an asymptotic formula for the relativistic spin network amplitude for a 4-simplex is given. The amplitude depends on specified areas for each two-dimensional face in the 4-simplex. The asymptotic…

The connection formulae provide a systematic way to compute physical quantities, such as the quasinormal modes, Green functions, in blackhole perturbation theories. In this work, we test whether it is possible to consistently take the…

A scalar field obeying a Lorentz invariant higher order wave equation, is minimally coupled to the electromagnetic field. The propagator and vertex factors for the Feynman diagrams, are determined. As an example we write down the matrix…

We classify the local asymptotic behavior of positive singular solutions to a class of subcritical sixth order equations on the punctured ball. Initially, using a version of the integral moving spheres technique, we prove that solutions are…

We develop a new method that allows us to map models of interacting fermions onto bosonic models describing collective excitations in an arbitrary dimension. This mapping becomes exact in the thermodynamic continuous time limit. The boson…