Symmetry Identities of Changhee Polynomials of Type Two

Jeong, Joohee; Kang, Dong-Jin; Rim, Seog-Hoon

doi:10.3390/sym10120740

Cited by 5 publications

(3 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For the derivation of those identities, we introduced certain quotients of bosonic p-adic and fermionic p-adic integrals on Z p , which have built-in symmetries. We note that this idea of using certain quotients of p-adic integrals has produced abundant symmetric identities (see [5,7,8,[18][19][20][21] and references therein).…”

Section: Discussionmentioning

confidence: 99%

Identities of Symmetry for Type 2 Bernoulli and Euler Polynomials

Ким

Kim

et al. 2019

Symmetry

View full text Add to dashboard Cite

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.

show abstract

Section: Discussionmentioning

confidence: 99%

Identities of Symmetry for Type 2 Bernoulli and Euler Polynomials

Ким

Kim

et al. 2019

Symmetry

View full text Add to dashboard Cite

show abstract

“…Alternatively, the sequence {Ch n (z)} ∞ n=0 is defined by means of the generating functions (see [6,28,29]):…”

Section: The Complex Changhee Polynomialsmentioning

confidence: 99%

A Class of Sheffer Sequences of Some Complex Polynomials and Their Degenerate Types

Kim

2019

Mathematics

View full text Add to dashboard Cite

We study some properties of Sheffer sequences for some special polynomials with complex Changhee and Daehee polynomials introducing their complex versions of the polynomials and splitting them into real and imaginary parts using trigonometric polynomial sequences. Moreover, considering their degenerate types of Sheffer sequences based on umbral composition, we present some useful expressions, properties, and examples about complex versions of the degenerate polynomials.

show abstract

“…(cf. [49], see also [40], [41]). The Peters polynomials s k (x; λ, µ) are defined by means of the following generating function:…”

Section: Generating Functions For Special Numbers and Polynomialsmentioning

confidence: 99%

Analysis of the p-adic q-Volkenborn integrals: An approach to generalized Apostol-type special numbers and polynomials and their applications

Şimşek

2016

Cogent Mathematics

View full text Add to dashboard Cite

The main objective of this article is to give and classify new formulas of p-adic integrals and blend these formulas with previously well known formulas. Therefore, this article gives briefly the formulas of p-adic integrals which were found previously, as well as applying the integral equations to the generating functions and other special functions, giving proofs of the new interesting and novel formulas. The p-adic integral formulas provided in this article contain several important well-known families of special numbers and special polynomials such as the Bernoulli numbers and polynomials, the Euler numbers and polynomials, the Stirling numbers, the Lah numbers, the Peters numbers and polynomials, the central factorial numbers, the Daehee numbers and polynomials, the Changhee numbers and polynomials, the Harmonic numbers, the Fubini numbers, combinatorial numbers and sums. In addition, we defined two new sequences containing the Bernoulli numbers and Euler numbers. These two sequences include central factorial numbers, Bernoulli numbers and Euler numbers. Some computation formulas and identities for these sequences are given. Finally we give further remarks, observations and comments related to content of this paper.

show abstract

Symmetry Identities of Changhee Polynomials of Type Two

Cited by 5 publications

References 14 publications

Identities of Symmetry for Type 2 Bernoulli and Euler Polynomials

Identities of Symmetry for Type 2 Bernoulli and Euler Polynomials

A Class of Sheffer Sequences of Some Complex Polynomials and Their Degenerate Types

Analysis of the p-adic q-Volkenborn integrals: An approach to generalized Apostol-type special numbers and polynomials and their applications

Contact Info

Product

Resources

About