scholarly journals Some New Classes of Generalized Apostol-Euler and Apostol-Genocchi Polynomials

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
R. Tremblay ◽  
S. Gaboury ◽  
B.-J. Fugère
Keyword(s):  
Addition Theorem ◽  
Euler Polynomials ◽  
Addition Formula ◽  
New Class ◽  
Genocchi Polynomials

The main object of this paper is to introduce and investigate two new classes of generalized Apostol-Euler and Apostol-Genocchi polynomials. In particular, we obtain a new addition formula for the new class of the generalized Apostol-Euler polynomials. We also give an extension and some analogues of the Srivastava-Pintér addition theorem obtained in the works by Srivastava and Pintér (2004) and R. Tremblay, S. Gaboury, B.-J. Fugère, and Tremblay et al. (2011). for both classes.

scholarly journals Some Identities on the Generalizedq-Bernoulli,q-Euler, andq-Genocchi Polynomials

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Daeyeoul Kim ◽  
Burak Kurt ◽  
Veli Kurt
Keyword(s):  
Recurrence Relations ◽  
Analogous Result ◽  
Bernoulli Polynomials ◽  
Addition Theorem ◽  
Euler Polynomials ◽  
Genocchi Polynomials

Mahmudov (2012, 2013) introduced and investigated someq-extensions of theq-Bernoulli polynomialsℬn,qαx,yof orderα, theq-Euler polynomialsℰn,qαx,yof orderα, and theq-Genocchi polynomials𝒢n,qαx,yof orderα. In this paper, we give some identities forℬn,qαx,y,𝒢n,qαx,y, andℰn,qαx,yand the recurrence relations between these polynomials. This is an analogous result to theq-extension of the Srivastava-Pintér addition theorem in Mahmudov (2013).

scholarly journals Some identities and recurrence relations on the two variables Bernoulli, Euler and Genocchi polynomials

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1757-1765
Author(s):  
Veli Kurt ◽  
Burak Kurt
Keyword(s):  
Recurrence Relation ◽  
Recurrence Relations ◽  
Bernoulli Polynomials ◽  
Addition Theorem ◽  
Euler Polynomials ◽  
Genocchi Polynomials

Mahmudov in ([16], [17], [18]) introduced and investigated some q-extensions of the q-Bernoulli polynomials B(?)n,q (x,y) of order ?, the q-Euler polynomials ?(?)n,q (x,y) of order ? and the q-Genocchi polynomials G(?)n,q (x,y) of order ?. In this article, we give some identities for the q-Bernoulli polynomials, q-Euler polynomials and q-Genocchi polynomials and the recurrence relation between these polynomials. We give a different form of the analogue of the Srivastava-Pint?r addition theorem.

scholarly journals -Analogues of the Bernoulli and Genocchi Polynomials and the Srivastava-Pintér Addition Theorems

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
N. I. Mahmudov
Keyword(s):  
Addition Theorem ◽  
Addition Theorems ◽  
New Class ◽  
Genocchi Polynomials

The main purpose of this paper is to introduce and investigate a new class of generalized Bernoulli and Genocchi polynomials based on the -integers. The -analogues of well-known formulas are derived. The -analogue of the Srivastava-Pintér addition theorem is obtained.

scholarly journals Some New Classes of Generalized Hermite-Based Apostol-Euler and Apostol-Genocchi Polynomials

2015 ◽  
Vol 55 (1) ◽  
pp. 153-170 ◽  
Author(s):  
M. A. Pathan ◽  
Waseem A. Khan
Keyword(s):  
Generating Functions ◽  
Euler Polynomials ◽  
New Class ◽  
Genocchi Polynomials ◽  
Summation Formulae

Abstract In this paper, we introduce a new class of generalized Apostol-Hermite-Euler polynomials and Apostol-Hermite-Genocchi polynomials and derive some implicit summation formulae by applying the generating functions. These results extend some known summations and identities of generalized Hermite-Euler polynomials studied by Dattoli et al, Kurt and Pathan.

scholarly journals Construction of the Type 2 Degenerate Multi-Poly-Euler Polynomials and Numbers

2020 ◽  
Author(s):  
Waseem Ahmad Khan ◽  
Mehmet Acikgoz ◽  
Ugur Duran
Keyword(s):  
Linear Combination ◽  
Stirling Numbers ◽  
Euler Polynomials ◽  
Addition Formula ◽  
New Class ◽  
Whitney Numbers ◽  
Derivative Formula ◽  
Euler Polynomials And Numbers ◽  
Special Case

In this paper, we consider a new class of polynomials which is called the multi-poly-Euler polynomials. Then, we investigate their some properties and relations. We provide that the type 2 degenerate multi-poly-Euler polynomials equals a linear combination of the degenerate Euler polynomials of higher order and the degenerate Stirling numbers of the first kind. Moreover, we provide an addition formula and a derivative formula. Furthermore, in a special case, we acquire a correlation between the type 2 degenerate multi-poly-Euler polynomials and degenerate Whitney numbers.

scholarly journals Some Properties of $Q$-Hermite Fubini Numbers and Polynomials

2019 ◽  
Author(s):  
Waseem A. Khan
Keyword(s):  
Generating Functions ◽  
Hermite Polynomials ◽  
Bernoulli Polynomials ◽  
Stirling Numbers ◽  
Euler Polynomials ◽  
New Class ◽  
Genocchi Polynomials ◽  
Summation Formulas

The main purpose of this paper is to introduce a new class of $q$-Hermite-Fubini numbers and polynomials by combining the $q$-Hermite polynomials and $q$-Fubini polynomials. By using generating functions for these numbers and polynomials, we derive some alternative summation formulas including powers of consecutive $q$-integers.  Also, we establish some relationships for $q$-Hermite-Fubini polynomials associated with $q$-Bernoulli polynomials, $q$-Euler polynomials and $q$-Genocchi polynomials and $q$-Stirling numbers of the second kind.

scholarly journals A Note on $(P,Q)$-Analogue Type of Fubini Numbers and Polynomials

2019 ◽  
Author(s):  
Waseem A. Khan
Keyword(s):  
Bernoulli Polynomials ◽  
Stirling Numbers ◽  
Euler Polynomials ◽  
New Class ◽  
Genocchi Polynomials ◽  
Summation Formulas

In this paper, we introduce a new class of  $(p,q)$-analogue type of Fubini numbers and polynomials and investigate some properties of these polynomials. We establish summation formulas of these polynomials by summation techniques series. Furthermore, we consider some relationships for  $(p,q)$-Fubini polynomials associated with $(p,q)$-Bernoulli polynomials, $(p,q)$-Euler polynomials and $(p,q)$-Genocchi polynomials and $(p,q)$-Stirling numbers of the second kind.

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