Related papers: Some inequalities for alternating Kurepa's functio…
In this paper we consider Kurepa's function $K(z)$ \cite{Kurepa_71}. We give some recurrent relations for Kurepa's function via appropriate sequences of rational functions and gamma function. Also, we give some inequalities for Kurepa's…
In this paper we consider the functional equation for alternating factorial sum and some of its particular solutions (alternating Kurepa's function $A(z)$ from [Petojevic_02] and function $A_{1}(z)$). We determine an extension of domain of…
In this paper we consider the functional equation for factorial sum and its particular solutions (Kurepa's function $K(z)$ \cite{Kurepa_71} and function $K_{1}(z)$). We determine an extension of domain of functions $K(z)$ and $K_{1}(z)$ in…
In this paper we consider some analytical relations between gamma function $\Gamma(z)$ and related functions such as the Kurepa's function $K(z)$ and alternating Kurepa's function $A(z)$. It is well-known in the physics that the Casimir…
In this paper, we construct generating functions of alternating sums for the Arakawa-Kaneko zeta values. From the expressions, we show alternating sum formulas for them. Based on these results, we apply the same method to other zeta values.
We give new proofs of two functional relations for the alternating analogues of Tornheim's double zeta function. Using the functional relations, we give new proofs of some evaluation formulas found by H. Tsumura for these alternating…
We consider the alternating zeta function and the alternating $L$-function of a graph $G$, and express them by using the Ihara zeta function of $G$. Next, we define a generalized alternating zeta function of a graph, and express the…
The alternating zeta function zeta*(s) = 1 - 2^{-s} + 3^{-s} - ... is related to the Riemann zeta function by the identity (1-2^{1-s})zeta(s) = zeta*(s). We deduce the vanishing of zeta*(s) at each nonreal zero of the factor 1-2^{1-s}…
As well known, the study of Riemanns zeta function {\zeta}(s) involves the related entire function {\xi}(s). A close relative of {\zeta}(s) is the alternating zeta function {\eta}(s). Similar to {\zeta}(s), also {\eta}(s) has a…
In the article [Petojevic 2006], A. Petojevi\' c verified useful properties of the $K_{i}(z)$ functions which generalize Kurepa's [Kurepa 1971] left factorial function. In this note, we present simplified proofs of two of these results and…
An analysis of the zeta and gamma function is presented, using elementary functions like [] and {}, a general formula for the angle of zeta(1/2 + i*n) is found and the same for the gamma function.
Functions satisfying the functional equation \begin{align*} \sum_{r=0}^{n-1} (-1)^r f(x+ry, ny) = f(x,y), \quad \text{for any positive odd integer $n$}, \end{align*} are named the alternating invariant functions. Examples of such functions…
In this paper, we study some Euler-Ap\'ery-type series which involve central binomial coefficients and (generalized) harmonic numbers. In particular, we establish elegant explicit formulas of some series by iterated integrals and…
We study absolute zeta functions from the view point of a canonical normalization. We introduce the absolute Hurwitz zeta function for the normalization. In particular, we show that the theory of multiple gamma and sine functions gives good…
In this paper, we construct certain analogues of the Arakawa-Kaneko zeta functions. We prove functional relations between these functions and the Mordell-Tornheim multiple zeta functions. Furthermore we give some formulas among…
It is well-known that the Riemann zeta function does not satisfy any exact polynomial differential equation. Here we present numerical evidence for the existence of approximate polynomial dependencies between the values of the alternating…
We establish a connection between the subfactorial function S(n) and the left factorial function of Kurepa K(n). Some elementary properties and congruences of both functions are described. Finally, we give a calculated distribution of…
In this paper, we construct the alternating multiple q-zeta function(= Multiple Euler q-zeta function) and investigate their properties. Finally, we give some interesting functional eauations related to q-Euler polynomials.
Several relations are obtained among the Riemann zeta and Hurwitz zeta functions, as well as their products. A particular case of these relations give rise to a simple re-derivation if the important results of [11]. Also, a relation derived…
A new formula relating the analytic continuation of the Hurwitz zeta function to the Euler gamma function and a polylogarithmic function is presented. In particular, the values of the first derivative of the real part of the analytic…