Generating function, recurrence relations, differential relations

Recurrence Relations and Generating Functions

Recurrence Relations for Moment Generating Functions of Generalized Order Statistics Based on Doubly Truncated Class of Distributions

In this paper, we derived recurrence relations for joint moment generating functions of nonadjacent generalized order statistics (GOS) of random samples drawn from doubly truncated class of continuous distributions. Recurrence relations for joint moments of nonadjacent GOS (ordinary order statistics (OOS) and k-upper records (k-RVs) as special cases) are obtained. Single and product moment gene...

( 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...

Recurrence Relations for the Lerch Φ Function and Applications

Abstract. In this paper we present a simple method for deriving recurrence relations and we apply it to obtain two equations involving the Lerch Phi function and sums of Bernoulli and Euler polynomials. Connections between these results and those obtained by H.M. Srivastava, M.L. Glasser and V. Adamchik ([8]) are pointed out, emphasizing the usefulness of this approach with some meaningful exam...

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...