Related papers: Closed-form solution of a general three-term recur…
We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…
The goal of this paper is to present an algebraic approach to the basic results of the theory of linear recurrence relations. This approach is based on the ideas from the theory of representations of one endomorphisms (a special case of…
We obtain exact solutions to the class of parabolic partial differential equations of arbitrary dimensionality and with arbitrary potentials. The solutions are presented in a compact-form: as explicit mathematical expressions consisting of…
We introduce the notion of $\mathcal{N}=1$ abstract super loop equations, and provide two equivalent ways of solving them. The first approach is a recursive formalism that can be thought of as a supersymmetric generalization of the…
In this sequel to our recent note it is shown, in a unified manner, by making use of some basic properties of certain special functions, such as the Hurwitz zeta function, Lerch zeta function and Legendre chi function, that the values of…
We establish three-term recurrence relations for the ${}_1\phi_1$ and ${}_0\phi_1$ basic hypergeometric series involving multiplicative shifts of the parameters and the variable by integer powers of q. The coefficients of these recurrence…
In the present paper, the nonlinear differential equation of pendulum is investigated to find an exact closed form solution, satisfying governing equation as well as initial conditions. The new concepts used in the suggested method are…
We introduce the method of path-sums which is a tool for exactly evaluating a function of a discrete matrix with possibly non-commuting entries, based on the closed-form resummation of infinite families of terms in the corresponding Taylor…
In this paper we are concerned with a family of sums involving the floor function. With $r$ a non negative integer and $n$ and $m$ positive integers we consider the sums…
Infinite series of the type Sum{n=1,infinity}(alpha/2)_n_2F_1(-n, b; gamma; y)/(n n!) are investigated. Closed-form sums are obtained for alpha a positive integer alpha=1,2,3, ... The limiting case of b --> infinity, after y is replaced…
This study introduces a procedure to obtain general expressions, $y = f(x)$, subject to linear constraints on the function and its derivatives defined at specified values. These constrained expressions can be used describe functions with…
We combine the fixed-order evaluation of the $b\bar{b}$ sum rules with a non-relativistic effective-theory approach. The combined result for the $n$-th moment includes all terms suppressed with respect to the leading-order result by ${\cal…
We propose investigating a summation analog of the paradigm for parallel integration. We make some first steps towards an indefinite summation method applicable to summands that rationally depend on the summation index and a P-recursive…
The general solution to the Complex Bateman equation is constructed. It is given in implicit form in terms of a functional relationship for the unknown function. The known solution of the usual Bateman equation is recovered as a special…
An approach is developed to find approximate solutions to the restricted circular three body problem. The solution is useful in approximately describing the position vectors of three spherically symmetric masses, one of which has a much…
We state and prove three general formulas allowing to transform formal finite sums into formal continued fractions and apply them to generalize certain expansions in continued fractions given by Hone and Varona.
In this paper we present a method to pass from a recurrence relation having constant coefficients (in short, a C-recurrence) to a finite succession rule defining the same number sequence. We recall that succession rules are a recently…
We consider open, oriented 3-manifolds which are infinite connected sums of closed 3-manifolds. We introduce some topological invariants for these manifolds and obtain a classification in the case where there are only finitely many summands…
In this article, we report on an exact closed-form solution for the displacement at the surface of an elastic half-space elicited by a buried point source that acts at some point underneath that surface. This is commonly referred to as the…
In linear transport theory, three-dimensional equations reduce to one-dimensional equations by means of rotated reference frames. In this paper, we illustrate how the technique works and three-dimensional transport theories are obtained.