Certain Generating Function of Hermite-Bernoulli-Laguerre Polynomials

Khan, Nabiullah; Usman, Talha; Choi, Junesang

doi:10.17654/ms101040893

Cited by 9 publications

(11 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Furthermore, the generalized Laguerre poly-Genocchi polynomials L G (k) p (u, v, w) in Equation 20, being very general, can be specialized to yield various known polynomials and numbers, for example, Genocchi numbers G n , Genocchi polynomials G n (x), and Hermite-Genocchi polynomials H G n (u, v) (see Reference [12]). In this regard, the results presented here can be specialized to yield or be closely connected with some known identities and formulas (see, e.g., References [14][15][16][17][18][19][20][21]23,25]), and the references cited therein). Therefore, the results presented in this article could potentially be useful in problems that arise in the aforementioned fields.…”

Section: Discussionmentioning

confidence: 96%

See 1 more Smart Citation

A Study of Generalized Laguerre Poly-Genocchi Polynomials

2019

Self Cite

View full text Add to dashboard Cite

A variety of polynomials, their extensions, and variants, have been extensively investigated, mainly due to their potential applications in diverse research areas. Motivated by their importance and potential for applications in a variety of research fields, numerous polynomials and their extensions have recently been introduced and investigated. In this paper, we introduce generalized Laguerre poly-Genocchi polynomials and investigate some of their properties and identities, which were found to extend some known results. Among them, an implicit summation formula and addition-symmetry identities for generalized Laguerre poly-Genocchi polynomials are derived. The results presented here, being very general, are pointed out to reduce to yield formulas and identities for relatively simple polynomials and numbers.

show abstract

Section: Discussionmentioning

confidence: 96%

“…Symmetry identities involving various polynomials have been presented (e.g., References [10,[14][15][16][17][18][20][21][22]). As in the above-cited works, here we establish some addition-symmetry identities involving generalized Laguerre poly-Genocchi polynomials L G…”

Section: Addition-symmetry Identitiesmentioning

confidence: 99%

A Study of Generalized Laguerre Poly-Genocchi Polynomials

2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…n (x, y) (see [29]). In this regard, the results presented here can be specialized to yield or be closely connected with some known identities and formulas (see, e.g., [5,13,[18][19][20][21][22][23][24][27][28][29]40,41], and the references cited therein). Therefore, the results presented in this article seem to be potentially useful in arising problems of the aforementioned fields.…”

Section: Discussionmentioning

confidence: 99%

“…Khan et al [18][19][20][21][22][23][24], Yang [40], and Zhang and Yang [41] have established some interesting symmetry identities for various polynomials. Here we present certain symmetry identities for the generalized Laguerre-Bernoulli polynomials (20) in the following theorem.…”

Section: Symmetry Identities For the Generalized Laguerre-bernoulli Pmentioning

confidence: 99%

A new class of generalized polynomials associated with Laguerre and Bernoulli polynomials

Khan¹,

Usman²,

Choi³

2019

Turk J Math

Self Cite

View full text Add to dashboard Cite

Motivated by their importance and potential for applications in certain problems in number theory, combinatorics, classical and numerical analysis, and other fields of applied mathematics, a variety of polynomials and numbers with their variants and extensions have recently been introduced and investigated. In this paper, we aim to introduce generalized Laguerre-Bernoulli polynomials and investigate some of their properties such as explicit summation formulas, addition formulas, implicit formulas, and symmetry identities. Relevant connections of the results presented here with those relatively simple numbers and polynomials are considered.

show abstract

“…So it may imply that the polynomials in (1.23) are more general than those in (1.22). The process and methods used in this paper follow from those employed in such works as [5,13,[15][16][17] including, in particular, the very recent work [18].…”

Section: Introductionmentioning

confidence: 99%

A new class of generalized polynomials involving Laguerre and Euler polynomials

Khan

Usman

Choi

2021

Hacettepe Journal of Mathematics and Statistics

Self Cite

View full text Add to dashboard Cite

Motivated by their importance and potential for applications in a variety of research fields, recently, numerous polynomials and their extensions have been introduced and investigated. In this paper, we modify the known generating functions of polynomials, due to both Milne-Thomsons and Dere-Simsek, to introduce a new class of polynomials and present some involved properties. As obvious special cases of the newly introduced polynomials, we also introduce power sum-Laguerre-Hermite polynomials and generalized Laguerre and Euler polynomials and give certain involved identities and formulas. We point out that our main results, being very general, are specialised to yield a number of known and new identities involving relatively simple and familiar polynomials.

show abstract

Certain Generating Function of Hermite-Bernoulli-Laguerre Polynomials

Cited by 9 publications

References 0 publications

A Study of Generalized Laguerre Poly-Genocchi Polynomials

A Study of Generalized Laguerre Poly-Genocchi Polynomials

A new class of generalized polynomials associated with Laguerre and Bernoulli polynomials

A new class of generalized polynomials involving Laguerre and Euler polynomials

Contact Info

Product

Resources

About