38 research outputs found
Identities on the k-ary Lyndon words related to a family of zeta functions
The main aim of this paper is to investigate and introduce relations between
the numbers of k-ary Lyndon words and unified zeta-type functions which was
defined by Ozden et al [15, p. 2785]. Finally, we give some identities on
generating functions for the numbers of k-ary Lyndon words and some special
numbers and polynomials such as the Apostol-Bernoulli numbers and polynomials,
Frobenius-Euler numbers, Euler numbers and Bernoulli numbers.Comment: 9 page
Interpolation function of the genocchi type polynomials
The main purpose of this paper is to construct not only generating functions
of the new approach Genocchi type numbers and polynomials but also
interpolation function of these numbers and polynomials which are related to a,
b, c arbitrary positive real parameters. We prove multiplication theorem of
these polynomials. Furthermore, we give some identities and applications
associated with these numbers, polynomials and their interpolation functions.Comment: 14 page
Some results on q-Hermite based hybrid polynomials
In this article, a hybrid class of the q-Hermite based Apostol type Frobenius-Euler polynomials is introduced by means of generating function and series representation. Several important formulas and recurrence relations for these polynomials are derived via different generating function methods. Further, the 2D q-Hermite based Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials are introduced and important relations for these polynomials are also established. Finally, a new class of the 2D q-Hermite based Appell polynomials is investigated as the generalization of the above polynomials. The determinant definitions for the 2D q-Hermite based Appell and related polynomials are also explored
Existence and reduction of generalized Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials
summary:One can find in the mathematical literature many recent papers studying the generalized Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials, defined by means of generating functions. In this article we clarify the range of parameters in which these definitions are valid and when they provide essentially different families of polynomials. In particular, we show that, up to multiplicative constants, it is enough to take as the “main family” those given by and as an “exceptional family” both of these for