Affiliation:
1. Department of Applied Mathematics , Faculty of Engineering and Technology , Aligarh Muslim University , Aligarh - 202002; and Department of Mathematics and Statistics, Integral University, Lucknow-226026 , India
2. Department of Applied Mathematics , Faculty of Engineering and Technology , Aligarh Muslim University , Aligarh - 202002 , India
3. Department of General Requirements , University of Technology and Applied Sciences , Sur - 411 , Oman
4. Department of Mathematics , Dongguk University , Gyeongju 38066 , Republic of Korea
Abstract
Abstract
The introduction of two-parameter
(
p
,
q
)
{(p,q)}
-calculus and Lie algebras in 1991
has spurred a wave of recent research into
(
p
,
q
)
{(p,q)}
-special polynomials, including
(
p
,
q
)
{(p,q)}
-Bernoulli,
(
p
,
q
)
{(p,q)}
-Euler,
(
p
,
q
)
{(p,q)}
-Genocchi and
(
p
,
q
)
{(p,q)}
-Frobenius–Euler polynomials.
These investigations have been carried out by numerous researchers in order to uncover a wide range of identities associated with these polynomials and applications. In this article, we aim to introduce
(
p
,
q
)
{(p,q)}
-sine and
(
p
,
q
)
{(p,q)}
-cosine based λ-array type polynomials and derive numerous properties of these polynomials
such as
(
p
,
q
)
{(p,q)}
-integral representations,
(
p
,
q
)
{(p,q)}
-partial derivative formulae and
(
p
,
q
)
{(p,q)}
-addition formulae.
It is worth noting that the utilization of the
(
p
,
q
)
{(p,q)}
-polynomials introduced in this study, along with other
(
p
,
q
)
{(p,q)}
-polynomials, can lead to the derivation of various identities that differ from the ones presented here.
Subject
Applied Mathematics,Numerical Analysis,Analysis
Reference39 articles.
1. A. Belafhal, H. Benzehoua, A. Balhamri and T. Usman,
An advanced method for evaluating Lommel integral and its application in marine environment,
J. Comput. Appl. Math. 416 (2022), Paper No. 114600.
2. A. Belafhal, H. Benzehoua and T. Usman,
Certain integral transforms and their application to generate new Laser waves: Exton–Gaussian beams,
Adv. Math. Models Appl. 6 (2021), no. 3, 206–217.
3. A. Belafhal, S. Chib, F. Khannous and T. Usman,
Evaluation of integral transforms using special functions with applications to biological tissues,
Comput. Appl. Math. 40 (2021), no. 4, Paper No. 156.
4. A. Belafhal, E. M. El Halba and T. Usman,
An integral transform involving the product of Bessel functions and Whittaker function and its application,
Int. J. Appl. Comput. Math. 6 (2020), no. 6, Paper No. 177.
5. A. Belafhal, E. M. El Halba and T. Usman,
A note on some representations of Appell and Horn functions,
Adv. Stud. Contemp. Math. (Kyungshang) 30 (2020), 5–16.
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献