Relations Between Contiguous Generalized Legendre Associated Functions (Recurrence Formulas).

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...

Integrals of polylogarithmic functions, recurrence relations, and associated Euler sums

We show that integrals of the form ∫ 1 0 xLip(x)Liq(x)dx (m ≥ −2, p, q ≥ 1) and ∫ 1 0 log(x)Lip(x)Liq(x) x dx (p, q, r ≥ 1) satisfy certain recurrence relations which allow us to write them in terms of Euler sums. From this we prove that, in the first case for all m, p, q and in the second case when p+ q+ r is even, these integrals are reducible to zeta values. In the case of odd p+q+r, we comb...

Recurrence Relations and Generating Functions

Recurrence Relations for Quotient Moment of Generalized Pareto Distribution Based on Generalized Order Statistics and Characterization

Generalized Pareto distribution play an important role in reliability, extreme value theory, and other branches of applied probability and statistics. This family of distributions includes exponential distribution, Pareto distribution, and Power distribution. In this paper, we established exact expressions and recurrence relations satisfied by the quotient moments of generalized order statistic...

Some Asymptotic Formulas on Generalized Divisor Functions

1 . Throughout this paper, we use the following notation : c•1 , c2 , . . ., X0 , X1 , . . . denote positive absolute constants. We denote the number of elements of the finite set S by BSI . We write ex =exp (x) . We denote the least prime factor of n by p(n) . We write pall n if pain but pa+1 f n . v(n) denotes the number of the distinct prime factors of n, while the number of all the prime fa...