scholarly journals New construction of type 2 degenerate central Fubini polynomials with their certain properties

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Sunil Kumar Sharma ◽  
Waseem A. Khan ◽  
Serkan Araci ◽  
Sameh S. Ahmed
Keyword(s):  
Integral Equations ◽  
Euler Numbers ◽  
Central Factorial Numbers ◽  
New Construction ◽  
Degenerate Version

Abstract Kim et al. (Proc. Jangjeon Math. Soc. 21(4):589–598, 2018) have studied the central Fubini polynomials associated with central factorial numbers of the second kind. Motivated by their work, we introduce degenerate version of the central Fubini polynomials. We show that these polynomials can be represented by the fermionic p-adic integral on $\mathbb{Z}_{p}$ Z p . From the fermionic p-adic integral equations, we derive some new properties related to degenerate central factorial numbers of the second kind and degenerate Euler numbers of the second kind.

Identities related to special polynomials and combinatorial numbers

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4833-4844 ◽  
Author(s):  
Eda Yuluklu ◽  
Yilmaz Simsek ◽  
Takao Komatsu
Keyword(s):  
Generating Functions ◽  
Functional Equations ◽  
Stirling Numbers ◽  
Bernoulli Numbers ◽  
Euler Numbers ◽  
Special Polynomials ◽  
Central Factorial Numbers

The aim of this paper is to give some new identities and relations related to the some families of special numbers such as the Bernoulli numbers, the Euler numbers, the Stirling numbers of the first and second kinds, the central factorial numbers and also the numbers y1(n,k,?) and y2(n,k,?) which are given Simsek [31]. Our method is related to the functional equations of the generating functions and the fermionic and bosonic p-adic Volkenborn integral on Zp. Finally, we give remarks and comments on our results.

scholarly journals Integral equations of biharmonic constant π₁-slope curves according to type-2 Bishop frame in the SOL space

2013 ◽  
Vol 31 (2) ◽  
pp. 205 ◽  
Author(s):  
Talat Körpinar ◽  
Essin Turhan
Keyword(s):  
Integral Equations ◽  
Bishop Frame ◽  
Sol Space

In this paper, we study biharmonic constant Π₁- slope curves according to type-2 Bishop frame in the SOL³. We characterize the biharmonic constant Π₁- slope curves in terms of their Bishop curvatures. Finally, we find out their explicit parametric integral equations in the SOL³.

scholarly journals Identities Involvingq-Bernoulli andq-Euler Numbers

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
D. S. Kim ◽  
T. Kim ◽  
J. Choi ◽  
Y. H. Kim
Keyword(s):  
Integral Equations ◽  
Euler Numbers

We give some identities on theq-Bernoulli andq-Euler numbers by usingp-adic integral equations onℤp.

scholarly journals Arithmetic Identities Involving Bernoulli and Euler Numbers

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
H.-M. Kim ◽  
D. S. Kim
Keyword(s):  
Integral Equations ◽  
Euler Numbers

The purpose of this paper is to give some arithmatic identities for the Bernoulli and Euler numbers. These identities are derived from the severalp-adic integral equations onℤp.

scholarly journals Some Properties of a Sequence Similar to Generalized Euler Numbers

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Haiqing Wang ◽  
Guodong Liu
Keyword(s):  
Generating Function ◽  
Stirling Numbers ◽  
Euler Polynomials ◽  
Euler Numbers ◽  
Explicit Formulas ◽  
Central Factorial Numbers

We introduce the sequence {Un(x)} given by generating function (1/(et+e-t-1))x=∑n=0∞Un(x)(tn/n!)  (|t|<(1/3)π,1x:=1) and establish some explicit formulas for the sequence {Un(x)}. Several identities involving the sequence {Un(x)}, Stirling numbers, Euler polynomials, and the central factorial numbers are also presented.

scholarly journals New families of special numbers for computing negative order Euler numbers and related numbers and polynomials

2018 ◽  
Vol 12 (1) ◽  
pp. 1-35 ◽  
Author(s):  
Yilmaz Simsek
Keyword(s):  
Generating Functions ◽  
Recurrence Relations ◽  
Bernstein Polynomials ◽  
Fibonacci Numbers ◽  
Stirling Numbers ◽  
Euler Numbers ◽  
Open Questions ◽  
Negative Order ◽  
Central Factorial Numbers ◽  
Probability And Statistics

The main purpose of this paper is to construct new families of special numbers with their generating functions. These numbers are related to many well-known numbers, which are Bernoulli numbers, Fibonacci numbers, Lucas numbers, Stirling numbers of the second kind and central factorial numbers. Our other inspiration of this paper is related to the Golombek's problem [15] "Aufgabe 1088. El. Math., 49 (1994), 126-127". Our first numbers are not only related to the Golombek's problem, but also computation of the negative order Euler numbers. We compute a few values of the numbers which are given by tables. We give some applications in probability and statistics. That is, special values of mathematical expectation of the binomial distribution and the Bernstein polynomials give us the value of our numbers. Taking derivative of our generating functions, we give partial differential equations and also functional equations. By using these equations, we derive recurrence relations and some formulas of our numbers. Moreover, we come up with a conjecture with two open questions related to our new numbers. We give two algorithms for computation of our numbers. We also give some combinatorial applications, further remarks on our new numbers and their generating functions.

scholarly journals Identities of Symmetry for Type 2 Bernoulli and Euler Polynomials

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 613 ◽  
Author(s):  
Dae San Kim ◽  
Han Young Kim ◽  
Dojin Kim ◽  
Taekyun Kim
Keyword(s):  
Prime Number ◽  
Random Variables ◽  
Bernoulli Polynomials ◽  
Euler Polynomials ◽  
Euler Numbers ◽  
Power Sums ◽  
Symmetric Identities ◽  
Positive Integers

The main purpose of this paper is to give several identities of symmetry for type 2 Bernoulli and Euler polynomials by considering certain quotients of bosonic p-adic and fermionic p-adic integrals on Z p , where p is an odd prime number. Indeed, they are symmetric identities involving type 2 Bernoulli polynomials and power sums of consecutive odd positive integers, and the ones involving type 2 Euler polynomials and alternating power sums of odd positive integers. Furthermore, we consider two random variables created from random variables having Laplace distributions and show their moments are given in terms of the type 2 Bernoulli and Euler numbers.

scholarly journals A Research on a Certain Family of Numbers and Polynomials Related to Stirling Numbers, Central Factorial Numbers, and Euler Numbers

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
J. Y. Kang ◽  
C. S. Ryoo
Keyword(s):  
Complex Plane ◽  
Stirling Numbers ◽  
Euler Numbers ◽  
Interesting Phenomenon ◽  
Genocchi Numbers ◽  
Central Factorial Numbers ◽  
Definition Of

Recently, many mathematicians have studied different kinds of the Euler, Bernoulli, and Genocchi numbers and polynomials. In this paper, we give another definition of polynomialsŨn(x). We observe an interesting phenomenon of “scattering” of the zeros of the polynomialsŨn(x)in complex plane. We find out some identities and properties related to polynomialsŨn(x). Finally, we also derive interesting relations between polynomialsŨn(x), Stirling numbers, central factorial numbers, and Euler numbers.

scholarly journals Combinatorial identities and sums for special numbers and polynomials

Filomat ◽  
2018 ◽  
Vol 32 (20) ◽  
pp. 6869-6877
Author(s):  
Yilmaz Simsek
Keyword(s):  
Partial Differential Equations ◽  
Generating Functions ◽  
Functional Equations ◽  
Stirling Numbers ◽  
Euler Numbers ◽  
Array Polynomials ◽  
Central Factorial Numbers ◽  
Special Numbers And Polynomials ◽  
Combinatorial Sums ◽  
Computation Algorithms

In this paper, by using some families of special numbers and polynomials with their generating functions and functional equations, we derive many new identities and relations related to these numbers and polynomials. These results are associated with well-known numbers and polynomials such as Euler numbers, Stirling numbers of the second kind, central factorial numbers and array polynomials. Furthermore, by using higher-order partial differential equations, we derive some combinatorial sums and identities. Finally, we give two computation algorithms for Euler numbers and central factorial numbers.

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