Recurrence Relations for the Lerch Φ Function and Applications
نویسنده
چکیده
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 examples.
منابع مشابه
Higher Order Moments and Recurrence Relations of Order Statistics from the Exponentiated Gamma Distribution
Order statistics arising from exponentiated gamma (EG) distribution are considered. Closed from expressions for the single and double moments of order statistics are derived. Measures of skewness and kurtosis of the probability density function of the rth order statistic for different choices of r, n and /theta are presented. Recurrence relations between single and double moments of r...
متن کاملRecurrence 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...
متن کاملRecurrences and explicit formulae for the expansion and connection coefficients in series of the product of two classical discrete orthogonal polynomials
Suppose that for an arbitrary function $f(x,y)$ of two discrete variables, we have the formal expansions. [f(x,y)=sumlimits_{m,n=0}^{infty }a_{m,n},P_{m}(x)P_{n}(y),] $$ x^{m}P_{j}(x)=sumlimits_{n=0}^{2m}a_{m,,n}(j)P_{j+m-n}(x),$$ we find the coefficients $b_{i,j}^{(p,q,ell ,,r)}$ in the expansion $$ x^{ell }y^{r},nabla _{x}^{p}nabla _{y}^{q},f(x,y)=x^{ell }y^{r}f^{(p,q)}(x,y) =sumli...
متن کاملGenerating relations and other results associated with some families of the extended Hurwitz-Lerch Zeta functions
ABSTRACT Motivated essentially by recent works by several authors (see, for example, Bin-Saad [Math J Okayama Univ 49:37-52, 2007] and Katsurada [Publ Inst Math (Beograd) (Nouvelle Ser) 62(76):13-25, 1997], the main objective in this paper is to present a systematic investigation of numerous interesting properties of some families of generating functions and their partial sums which are associa...
متن کاملGeometric Studies on Inequalities of Harmonic Functions in a Complex Field Based on ξ-Generalized Hurwitz-Lerch Zeta Function
Authors, define and establish a new subclass of harmonic regular schlicht functions (HSF) in the open unit disc through the use of the extended generalized Noor-type integral operator associated with the ξ-generalized Hurwitz-Lerch Zeta function (GHLZF). Furthermore, some geometric properties of this subclass are also studied.
متن کامل