Related papers: Smarandache Type Function Obtained by Duality

In the present paper, we introduce Eulerian polynomials attached to by using p-adic q-integral on Zp . Also, we give new interesting identities via the generating functions of Dirichlet's type of Eulerian polynomials. After, by applying…

In this paper, we give a generate function for the $\sigma_1$ function. Then we find some connections between the $\sigma_1$ function and the Ramanujan's tau function. We hope this connection will give some insights into the unsolved…

Using non-archimedean q-integrals on Zp defined in [15, 16], we define a new Changhee q-Euler polynomials and numbers which are different from those of Kim [7] and Carlitz [2]. We define generating functions of multiple q-Euler numbers and…

Recently, Kaneko and Tsumura introduced multiple $\widetilde{T}$-values, another kind of poly-Euler numbers and the related Arakawa-Kaneko type zeta function. It is shown that each of them satisfies similar formulas to those of multiple…

A motivated q-extension of the values of the Riemann zeta function at positive integers is presented. Several irrationality and transcendence results as well as new general problems for these q-zeta values are stated.

We define discrete generating series for arbitrary functions \( f \colon \mathbb{Z}^n \rightarrow \mathbb{C} \) and derive functional relations that these series satisfy. For linear difference equations with constant coefficients, we…

A multiple-valued function $f:X\to {\bf Q}_Q(Y)$ is essentially a rule assigning $Q$ unordered and non necessarily distinct elements of $Y$ to each element of $X$. We study the Lipschitz extension problem in this context by using two…

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.

The aim of this paper is to define new generating functions. By applying the Mellin transformation formula to these generating functions, we define q-analogue of Genocchi zeta function, q-analogue Hurwitz type Genocchi zeta function,…

In this paper we give the q-extension of Euler numbers which can be viewed as interpolating of the q-analogue of Euler zeta function ay negative integers, in the same way that Riemann zeta function interpolates Bernoulli numbers at negative…

We construct a pathwise calculus for functionals of integer-valued measures and use it to derive an martingale representation formula with respect to a large class of integer-valued random measures. Using these results, we extend the…

We define two finite q-analogs of certain multiple harmonic series with an arbitrary number of free parameters, and prove identities for these q-analogs, expressing them in terms of multiply nested sums involving the Gaussian binomial…

We compute the generating function for the characters of the irreducible representations of SU(n) whose associated Young diagrams have only two rows with the same number of boxes. The result is a rational determinantal expression in which…

We construct a large family of Fourier interpolation bases for functions analytic in a strip symmetric about the real line. Interesting examples involve the nontrivial zeros of the Riemann zeta function and other $L$-functions. We establish…

In this short paper, we show how to deduce several types of generating functions from Srivastava {\it et al} [Appl. Set-Valued Anal. Optim. {\bf 1} (2019), pp. 187-201.] by the method of $q$-difference equations. Moreover, we build…

We consider unitals of order $q$ with two points which are centers of translation groups of order $q$. The group $G$ generated by these translations induces a Moufang set on the block joining the two points. We show that $G$ is either…

We summarize the known useful and interesting results and formulas we have discovered so far in this collaborative article summarizing results from two related articles by Merca and Schmidt arriving at related so-termed Lambert series…

The Legendre type relation for the counting function of ordinary twin primes is reworked in terms of the inverse of the Riemann zeta function. Its analysis sheds light on the distribution of the zeros of the Riemann zeta function in the…

The additive analogues of Pseudo-Smarandache, Smarandache-simple functions and their duals have been recently studied by J. Sandor. In this note, we obtain q-analogue of Sandor's theorems.

We extend the recently developed theory of Roehrig and Zwegers on indefinite theta functions to prove certain power series are modular forms. As a consequence, we obtain several power series identities for powers of the generating function…