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Given finitely many consecutive terms of an infinite sequence, we discuss the construction of a polynomial difference equation that the sequence may satisfy. We also present a method to seek a candidate polynomial differential equation for…
The theory of formal power series and derivation is developed from the point of view of the power matrix. A Loewner equation for formal power series is introduced. We then show that the matrix exponential is surjective onto the group of…
Using a simple transfer matrix approach we have derived very long series expansions for the perimeter generating function of three-choice polygons. We find that all the terms in the generating function can be reproduced from a linear…
The field equations of Mannheim's theory of conformal gravity with dynamic mass generation are solved numerically in the interior and exterior regions of a model spherically symmetric sun with matched boundary conditions at the surface. The…
We show how to compute conformal blocks of operators in arbitrary Lorentz representations using the formalism described in arXiv:1905.00036 and arXiv:1905.00434, and present several explicit examples of blocks derived via this method. The…
We study the existence of singular separable solutions to a class of quasilinear equations with reaction term. In the 2-dim case, we use a dynamical system approach to construct our solutions.
By means of the generating function method, a linear recurrence relation is explicitly resolved. The solution is expressed in terms of the Stirling numbers of both the first and the second kind. Two remarkable pairs of combinatorial…
We use the flux attractor equations to study IIB supergravity compactifications with ISD fluxes. We show that the attractor equations determine not just the values of moduli fields, but also the masses of those moduli and the gravitino. We…
In the present work we study numerical solution of the radial Dirac equation in a specific case - ab-initio pseudopotential generating process - which is needed within the electronic structure calculations using a Density Functional Theory…
The form of the coefficients of power series expressions corresponding to solutions of Fuchsian differential equations (or their associated degenerated confluent forms) with n regular singular points is determined by solving the…
Power series in which the summand satisfies a linear recurrence relation with polynomial coefficients are shown to be the solution of a linear differential or algebraic equation. Solving the associated differential or algebraic equation…
We consider the Cauchy problem for homogeneous linear $q$-difference-differential equations with constant coefficients. We characterise convergent, $k$-summable and multisummable formal power series solutions in terms of analytic…
A generalization of the Gr\"{u}nwald difference approximation for fractional derivatives in terms of a real sequence and its generating function is presented. Properties of the generating function are derived for consistency and order of…
We determine explicit generators for a cohomology group constructed from a solution of a fuchsian linear differential equation and describe its relation with cohomology groups with coefficients in a local system. In the parameterized case,…
Power Series Solution method has been used traditionally for to solve Linear Differential Equations, in Ordinary and Partial form. But this method has been limited to this kind of problems. We present the solution of problems of Non Linear…
Let G be the space of generating functions of a periodic infinite order linear recurrence. In this paper we provide an explicit procedure for computing a basis of G.
In the previous work [2] (i.e., arXiv:2105.03385), we considered continuous solutions of an iterative equation involving the multiplication of iterates. In this paper, we continue to investigate this equation for differentiable solutions.…
Based on previous work we consturct an equation (Lagrange equation) and relate it with a system of generalized integrals and differential equations in such a way to provide useful evaluations and connections between them.
In this study, a recursive solution technique in conjunction with generalized integrating factors is presented and applied to address first and second order linear differential equations. This approach demonstrates practical utility in…
This note gives a few rapidly convergent series representations of the sums of divisors functions. These series have various applications such as exact evaluations of some power series, computing estimates and proving the existence results…