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
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