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.