scholarly journals On a degenerate q-Euler polynomials and numbers with weight

2019 ◽  
Vol 20 (03) ◽  
pp. 216-224
Author(s):  
Guhyun Na ◽  
Yunju Cho ◽  
Jin-Woo Park
Keyword(s):  
Euler Polynomials ◽  
Euler Polynomials And Numbers

scholarly journals A Note on a New Type of Degenerate poly-Euler Numbers and Polynomials

2020 ◽  
Author(s):  
Waseem Khan
Keyword(s):  
Arithmetic Function ◽  
Bernoulli Numbers ◽  
Euler Polynomials ◽  
Euler Numbers ◽  
Polylogarithm Function ◽  
Euler Numbers And Polynomials ◽  
Special Numbers And Polynomials ◽  
Euler Polynomials And Numbers ◽  
New Type ◽  
Logarithm Function

Kim-Kim [12] introduced the new type of degenerate Bernoulli numbers and polynomials arising from the degenerate logarithm function. In this paper, we introduce a new type of degenerate poly-Euler polynomials and numbers, are called degenerate poly-Euler polynomials and numbers, by using the degenerate polylogarithm function and derive several properties on the degenerate poly-Euler polynomials and numbers. In the last section, we also consider the degenerate unipoly-Euler polynomials attached to an arithmetic function, by using the degenerate polylogarithm function and investigate some identities of those polynomials. In particular, we give some new explicit expressions and identities of degenerate unipoly polynomials related to special numbers and polynomials.

scholarly journals Sums of Products of -Euler Polynomials and Numbers

2009 ◽  
Vol 2009 (1) ◽  
pp. 381324 ◽  
Author(s):  
Young-Hee Kim ◽  
Kyung-Won Hwang ◽  
Taekyun Kim
Keyword(s):  
Euler Polynomials ◽  
Euler Polynomials And Numbers ◽  
Sums Of Products

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 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.

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