Turkish Journal of Analysis and Number Theory

3

Authors: Serkan Araci, Mehmet Acikgoz, Armen Bagdasaryan, Erdoğan Şen

In the present paper, we deal mainly with arithmetic properties of Legendre polynomials by using their orthogonality property. We show that Legendre polynomials are proportional with Bernoulli, Euler, Hermite and Bernstein polynomials.

4

Authors: Erdoğan Şen, Mehmet Acikgoz, Serkan Araci

The p-adic log gamma functions associated with q-extensions of Genocchi and Euler polynomials with weight α were recently studied . By the same motivation, we aim in this paper to describe q-analogue of p-adic log gamma functions with weight alpha and beta. Moreover, we give relationship between p-adic q-log gamma functions with weight (α,β) and q-extension of Genocchi numbers with weight alpha and beta and modified q-Euler numbers with weight α.

4

Authors: Jin-Woo Park, Seog-Hoon Rim, Jongkyum Kwon

We consider the hyper-geometric Daehee numbrers and polynomials and investigate some properties of those numbers and polynomials.

5

Authors: Yashwant K. Panwar, B. Singh, V.K. Gupta

In this study, we present generalized Fibonacci polynomials. We have used their Binet’s formula and generating function to derive the identities. The proofs of the main theorems are based on special functions, simple algebra and give several interesting properties involving them.

6

Authors: Serkan Araci, Mehmet Acikgoz, Erdoğan Şen

In the present paper, we deal with multiple generalized Genocchi numbers and polynomials. Also, we introduce analytic interpolating function for the multiple generalized Genocchi numbers attached to χ at negative integers in complex plane and we de.ne the multiple Genocchi p-adic L-function. Finally, we derive the value of the partial derivative of our multiple p-adic l-function at s = 0.

6

Authors: Chii-Huei Yu

This article takes the mathematical software Maple as the auxiliary tool to study the partial differential problem of two types of multivariable functions. We can obtain the infinite series forms of any order partial derivatives of these two types of functions by using differentiation term by term theorem, and hence greatly reduce the difficulty of calculating their higher order partial derivative values. On the other hand, we propose two examples to do calculation practically. The research methods adopted in this study involved finding solutions through manual calculations and verifying our answers by using Maple.

10

Authors: H. M. Srivastava, Min-Jie Luo, R. K. Raina

In this paper, we study a certain class of generalized Hurwitz-Lerch zeta functions. We derive several new and useful properties of these generalized Hurwitz-Lerch zeta functions such as (for example) their partial differential equations, new series and Mellin-Barnes type contour integral representations involving Fox’s H-function and a pair of summation formulas. More importantly, by considering their application in Number Theory, we construct a new continuous analogue of Lippert’s Hurwitz measure. Some statistical applications are also given.