Related papers: On regularization of the Heun functions
The statement of the Riemann hypothesis makes sense for all global fields, not just the rational numbers. For function fields, it has a natural restatement in terms of the associated curve. Weil's work on the Riemann hypothesis for curves…
The quantum spectral curve equation associated to KP $\tau$-functions of hypergeometric type serving as generating functions for rationally weighted Hurwitz numbers is solved by generalized hypergeometric series. The basis elements spanning…
We study some thermodynamics quantities for the Klein-Gordon equation with a linear plus inverse-linear, scalar potential. We obtain the energy eigenvalues with the help of the quantization rule coming from the biconfluent Heun's equation.…
This article is a natural continuation of the paper Tiwari, D., Giordano, P., Hyperseries in the non-Archimedean ring of Colombeau generalized numbers in this journal. We study one variable hyper-power series by analyzing the notion of…
The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the…
We reconsider linear perturbations around general Friedmann - Lemaitre - Robertson - Walker (FLRW) cosmological backgrounds. Exploiting gauge freedom involving only time reparametrizations, we write down classical background solutions…
We consider the 2-dimensional spatially homogeneous Boltzmann equation for hard potentials. We assume that the initial condition is a probability measure that has some exponential moments and is not a Dirac mass. We prove some…
The classical Kramer sampling theorem establishes general conditions that allow the reconstruction of functions by mean of orthogonal sampling formulae. One major task in sampling theory is to find concrete, non trivial realizations of this…
We establish conditions for the discrete versions of logarithmic concavity and convexity of the higher order regularized basic hypergeometric function with respect simultaneous shift of all its parameters. For a particular case of Heine's…
Reduction formulas for sums of products of hypergeometric functions can be traced back to Euler. This topic has an intimate connection to summation and transformation formulas, contiguous relations and algebraic properties of the…
Let $(E)$ a homogeneous linear differential equation of order $n$ Fuchsien over $\mathbb{P}^{1}(\mathbb{C}) $. The idea of Riemann (1857) was to obtain the properties of solutions of (E) by studying the local system. Thus, he obtained some…
In a recent paper we introduced sine functions on commutative hypergroups. These functions are natural generalizations of those functions on groups which are products of additive and multiplicative homomorphisms. In this paper we describe…
Various regularization methods have been used to compute the self-force acting on a static particle in a static, curved spacetime. Many of these are based on Hadamard's two-point function in three dimensions. On the other hand, the…
The existence of singularities of the solution for a class of Lax equations is investigated using a development of the fac- torization method first proposed by Semenov-Tian-Shansky and Reymann [11], [9]. It is shown that the existence of a…
Many articles have recently been devoted to Mahler equations, partly because of their links with other branches of mathematics such as automata theory. Hahn series (a generalization of the Puiseux series allowing arbitrary exponents of the…
We analyze the performance of a variant of Newton method with quadratic regularization for solving composite convex minimization problems. At each step of our method, we choose regularization parameter proportional to a certain power of the…
This report provides Green's functions (classical propagators) of gravitational fields appearing in general relativity. The existence of Green's function of the wave equation in curved space with an indefinite metric is ensured owing to the…
We examine the series expansions of the solutions of the confluent Heun equation in terms of three different sets of the Kummer confluent hypergeometric functions. The coefficients of the expansions in general obey three-term recurrence…
A general framework is presented for the renormalization of Hamiltonians via a similarity transformation. Divergences in the similarity flow equations may be handled with dimensional regularization in this approach, and the resulting…
We obtain the exact solution of the Schr\"odinger equation for a particle (galaxy) moving in a Newtonian universe with a cosmological constant, which is given in terms of the biconfluent Heun functions. The first six Heun polynomials of the…