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Search Results (3)

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Keywords = q-generalized tangent polynomials and numbers

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22 pages, 5257 KB  
Article
q-Generalized Tangent Based Hybrid Polynomials
by Ghazala Yasmin, Hibah Islahi and Junesang Choi
Symmetry 2021, 13(5), 791; https://doi.org/10.3390/sym13050791 - 3 May 2021
Cited by 5 | Viewed by 2129
Abstract
In this paper, we incorporate two known polynomials to introduce so-called 2-variable q-generalized tangent based Apostol type Frobenius–Euler polynomials. Next we present a number of properties and formulas for these polynomials such as explicit expressions, series representations, summation formulas, addition formula, q [...] Read more.
In this paper, we incorporate two known polynomials to introduce so-called 2-variable q-generalized tangent based Apostol type Frobenius–Euler polynomials. Next we present a number of properties and formulas for these polynomials such as explicit expressions, series representations, summation formulas, addition formula, q-derivative and q-integral formulas, together with numerous particular cases of the new polynomials and their associated formulas demonstrated in two tables. Further, by using computer-aided programs (for example, Mathematica or Matlab), we draw graphs of some particular cases of the new polynomials, mainly, in order to observe in several angles how zeros of these polynomials are distributed and located. Lastly we provide numerous observations and questions which naturally arise amid the present investigation. Full article
(This article belongs to the Special Issue Recent Advances in Special Functions and Their Applications)
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20 pages, 741 KB  
Article
A Numerical Computation of Zeros of q-Generalized Tangent-Appell Polynomials
by Ghazala Yasmin, Cheon Seoung Ryoo and Hibah Islahi
Mathematics 2020, 8(3), 383; https://doi.org/10.3390/math8030383 - 9 Mar 2020
Cited by 6 | Viewed by 2276
Abstract
The intended objective of this study is to define and investigate a new class of q-generalized tangent-based Appell polynomials by combining the families of 2-variable q-generalized tangent polynomials and q-Appell polynomials. The investigation includes derivations of generating functions, series definitions, [...] Read more.
The intended objective of this study is to define and investigate a new class of q-generalized tangent-based Appell polynomials by combining the families of 2-variable q-generalized tangent polynomials and q-Appell polynomials. The investigation includes derivations of generating functions, series definitions, and several important properties and identities of the hybrid q-special polynomials. Further, the analogous study for the members of this q-hybrid family are illustrated. The graphical representation of its members is shown, and the distributions of zeros are displayed. Full article
(This article belongs to the Special Issue Special Functions and Applications)
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12 pages, 300 KB  
Article
Symmetric Identities for (P,Q)-Analogue of Tangent Zeta Function
by Cheon Seoung Ryoo
Symmetry 2018, 10(9), 395; https://doi.org/10.3390/sym10090395 - 11 Sep 2018
Cited by 6 | Viewed by 3628
Abstract
The goal of this paper is to define the ( p , q ) -analogue of tangent numbers and polynomials by generalizing the tangent numbers and polynomials and Carlitz-type q-tangent numbers and polynomials. We get some explicit formulas and properties in conjunction [...] Read more.
The goal of this paper is to define the ( p , q ) -analogue of tangent numbers and polynomials by generalizing the tangent numbers and polynomials and Carlitz-type q-tangent numbers and polynomials. We get some explicit formulas and properties in conjunction with ( p , q ) -analogue of tangent numbers and polynomials. We give some new symmetric identities for ( p , q ) -analogue of tangent polynomials by using ( p , q ) -tangent zeta function. Finally, we investigate the distribution and symmetry of the zero of ( p , q ) -analogue of tangent polynomials with numerical methods. Full article
(This article belongs to the Special Issue Integral Transforms and Operational Calculus)
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