scholarly journals Apostol Type (p, q)-Frobenius-Euler Polynomials and Numbers

2017 ◽  
Author(s):  
Ugur Duran ◽  
Mehmet Acikgoz
Keyword(s):  
Difference Equations ◽  
Recurrence Relations ◽  
Integral Representations ◽  
Euler Polynomials ◽  
Addition Theorems ◽  
Explicit Formulas ◽  
Euler Polynomials And Numbers ◽  
Appl Math

In the present paper, we introduce (p, q)-extension of Apostol type Frobenius-Euler polynomials and numbers and investigate some basic identities and properties for these polynomials and numbers, including addition theorems, difference equations, derivative properties, recurrence relations and so on. Then, we provide integral representations, explicit formulas and relations for these polynomials and numbers. Moreover, we discover (p, q)-extensions of Carlitz's result [L. Carlitz, Mat. Mag., 32 (1959), 247–260] and Srivastava and Pintér addition theorems in [H. M. Srivastava, A. Pinter, Appl. Math. Lett., 17 (2004), 375–380].

scholarly journals Certain Results on (p,q)-Hermite Based Apostol Type Frobenius-Euler Polynomials

2019 ◽  
Author(s):  
Waseem Khan ◽  
Idrees Ahmad Khan ◽  
Ugur Duran ◽  
Mehmet Acikgoz
Keyword(s):  
Difference Equations ◽  
Recurrence Relations ◽  
Stirling Numbers ◽  
Integral Representations ◽  
Euler Polynomials ◽  
Addition Theorems ◽  
Summation Formulas ◽  
Euler Polynomials And Numbers

In the present paper, the (p,q)-Hermite based Apostol type Frobenius-Euler polynomials and numbers are firstly considered and then diverse basic identities and properties for the mentioned polynomials and numbers, including addition theorems, difference equations, integral representations, derivative properties, recurrence relations. Moreover, we provide summation formulas and relations associated with the Stirling numbers of the second kind.

scholarly journals On Multi Poly-Genocchi Polynomials with Parameters a, b and c

2020 ◽  
Vol 13 (3) ◽  
pp. 444-458
Author(s):  
Roberto Bagsarsa Corcino ◽  
Mark Laurente ◽  
Mary Ann Ritzell Vega
Keyword(s):  
Recurrence Relations ◽  
Euler Polynomials ◽  
Explicit Formulas ◽  
Multiple Parameters ◽  
Genocchi Numbers ◽  
Genocchi Polynomials

Most identities of Genocchi numbers and polynomials are related to the well-knownBenoulli and Euler polynomials. In this paper, multi poly-Genocchi polynomials withparameters a, b and c are dened by means of multiple parameters polylogarithm. Several properties of these polynomials are established including some recurrence relations and explicit formulas.

scholarly journals A class of big (p,q)-Appell polynomials and their associated difference equations

Filomat ◽  
2019 ◽  
Vol 33 (10) ◽  
pp. 3085-3121
Author(s):  
H.M. Srivastava ◽  
B.Y. Yaşar ◽  
M.A. Özarslan
Keyword(s):  
Differential Equation ◽  
Difference Equation ◽  
Recurrence Relation ◽  
Difference Equations ◽  
Recurrence Relations ◽  
Bernoulli Polynomials ◽  
Equivalence Theorem ◽  
Euler Polynomials ◽  
Appell Polynomials ◽  
Special Case

In the present paper, we introduce and investigate the big (p,q)-Appell polynomials. We prove an equivalance theorem satisfied by the big (p, q)-Appell polynomials. As a special case of the big (p,q)- Appell polynomials, we present the corresponding equivalence theorem, recurrence relation and difference equation for the big q-Appell polynomials. We also present the equivalence theorem, recurrence relation and differential equation for the usual Appell polynomials. Moreover, for the big (p; q)-Bernoulli polynomials and the big (p; q)-Euler polynomials, we obtain recurrence relations and difference equations. In the special case when p = 1, we obtain recurrence relations and difference equations which are satisfied by the big q-Bernoulli polynomials and the big q-Euler polynomials. In the case when p = 1 and q ? 1-, the big (p,q)-Appell polynomials reduce to the usual Appell polynomials. Therefore, the recurrence relation and the difference equation obtained for the big (p; q)-Appell polynomials coincide with the recurrence relation and differential equation satisfied by the usual Appell polynomials. In the last section, we have chosen to also point out some obvious connections between the (p; q)-analysis and the classical q-analysis, which would show rather clearly that, in most cases, the transition from a known q-result to the corresponding (p,q)-result is fairly straightforward.

scholarly journals Notes on unified q-Apostol-type polynomials

Filomat ◽  
2016 ◽  
Vol 30 (4) ◽  
pp. 921-927 ◽  
Author(s):  
Burak Kurt
Keyword(s):  
Generating Functions ◽  
Recurrence Relations ◽  
Euler Polynomials ◽  
Addition Theorems ◽  
Genocchi Polynomials

Recently, many mathematicians (Karande and Thakare [6], Ozarslan [14], Ozden et. al. [15], El-Deouky et. al. [5]) have studied the unification of Bernoulli, Euler and Genocchi polynomials. They gave some recurrence relations and proved some theorems. Mahmudov [13] defined the new q-Apostol- Bernoulli and q-Apostol-Euler polynomials. Also he gave the analogous of the Srivastava-Pint?r addition theorems. Kurt [8] gave the new identities and some relations for these polynomials. In this work, we give some recurrence relations for the unified q-Apostol-type polynomials related to multiple sums. By using generating functions we derive many new identities and recurrence relations associated with the q-Apostol type Bernoulli, the q-Apostol-type Euler and the q-Apostol-type Genocchi polynomials and numbers and also the generalized Stirling type numbers of the second kind.

scholarly journals Certain identities, connection and explicit formulas for the Bernoulli and Euler numbers and the Riemann zeta-values

Analysis ◽  
2015 ◽  
Vol 35 (1) ◽  
Author(s):  
Semyon Yakubovich
Keyword(s):  
Zeta Function ◽  
Recurrence Relations ◽  
Integral Representations ◽  
Euler Numbers ◽  
Explicit Formulas ◽  
Zeta Values ◽  
Riemann Zeta ◽  
Riemann’S Zeta Function

AbstractVarious new identities, recurrence relations, integral representations, connection and explicit formulas are established for the Bernoulli and Euler numbers and the values of Riemann's zeta function ζ(

New family of Whitney numbers

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 309-320 ◽  
Author(s):  
B.S. El-Desouky ◽  
Nenad Cakic ◽  
F.A. Shiha
Keyword(s):  
Generating Functions ◽  
Recurrence Relations ◽  
Stirling Numbers ◽  
Explicit Formulas ◽  
Basic Properties ◽  
New Family ◽  
Whitney Numbers ◽  
Special Cases

In this paper we give a new family of numbers, called ??-Whitney numbers, which gives generalization of many types of Whitney numbers and Stirling numbers. Some basic properties of these numbers such as recurrence relations, explicit formulas and generating functions are given. Finally many interesting special cases are derived.

scholarly journals Note on the Hurwitz–Lerch Zeta Function of Two Variables

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1431
Author(s):  
Junesang Choi ◽  
Recep Şahin ◽  
Oğuz Yağcı ◽  
Dojin Kim
Keyword(s):  
Zeta Function ◽  
Generating Functions ◽  
Recurrence Relations ◽  
Zeta Functions ◽  
Integral Representations ◽  
Lerch Zeta Function ◽  
Derivative Formulas ◽  
The One ◽  
Function Of Two Variables

A number of generalized Hurwitz–Lerch zeta functions have been presented and investigated. In this study, by choosing a known extended Hurwitz–Lerch zeta function of two variables, which has been very recently presented, in a systematic way, we propose to establish certain formulas and representations for this extended Hurwitz–Lerch zeta function such as integral representations, generating functions, derivative formulas and recurrence relations. We also point out that the results presented here can be reduced to yield corresponding results for several less generalized Hurwitz–Lerch zeta functions than the extended Hurwitz–Lerch zeta function considered here. For further investigation, among possibly various more generalized Hurwitz–Lerch zeta functions than the one considered here, two more generalized settings are provided.

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