Recurrence relations in Padé—Hermite approximation

( Probabilistic ) Recurrence Relations

The performance attributes of a broad class of randomised algorithms can be described by a recurrence relation of the form T(x) = a(x)+T(H(x)), where a is a function and H(x) is a random variable. For instance, T(x) may describe the running time of such an algorithm on a problem of size x. Then T(x) is a random variable, whose distribution depends on the distribution of H(x). To give high proba...

Relativistic Kramers–pasternack Recurrence Relations

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...

Recurrence relations versus succession rules

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 ...

Recurrence Relations and Generating Functions

Recurrence relations and fast algorithms

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...