In this paper we explore some of the geometry that lies behind real linear, second order, constant coefficient, recurrence relation (1) where a and b are numbers. Readers will be familiar with standard method solving relation, and, to avoid trivial cases, shall assume ab ≠ 0. The auxiliary equation t 2 = at + has two (possibly complex) solutions most general solution is given by (i) when distin...

Recently we have evaluated the matrix elements 〈Orp〉, where O = {1, β, iαnβ} are the standard Dirac matrix operators and the angular brackets denote the quantum-mechanical average for the relativistic Coulomb problem, in terms of generalized hypergeometric functions 3F2 (1) for all suitable powers and established two sets of Pasternack-type matrix identities for these integrals. The correspondi...

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 studied tool for the enumeration of combinatorial objects related to the ECO method. We also discuss the applicability of our method as a test for the positivity ...

We construct fast algorithms for evaluating transforms associated with families of functions which satisfy recurrence relations. These include algorithms both for computing the coefficients in linear combinations of the functions, given the values of these linear combinations at certain points, and, vice versa, for evaluating such linear combinations at those points, given the coefficients in t...

Recurrence relations with minimization and maximization, called minmax recurrence relations are commonly encountered in the analysis of algorithms. In this paper we present the solution of one such challenging recurrence relation. We characterize the optimal partition sizes as well as derive the order of complexity of the overall recurrence relation. It is proved that ad hoc equal partitioning ...