TY - JOUR AU - S. Khan AU - M. Riyasat AU - Sh. A. Wani PY - 2021/03/19 Y2 - 2024/03/28 TI - Differential and integral equations for Legendre – Laguerre based hybrid polynomials JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 73 IS - 3 SE - Research articles DO - 10.37863/umzh.v73i3.894 UR - https://umj.imath.kiev.ua/index.php/umj/article/view/894 AB - UDC 517.9 In this article, a hybrid family of three-variable Legendre – Laguerre – Appell polynomials is explored and their properties including the series expansions, determinant forms, recurrence relations, shift operators, followed by differential, integro-differential and partial differential equations are established. The analogous results for the three-variable Hermite – Laguerre – Appell polynomials are deduced. Certain examples in terms of Legendre – Laguerre – Bernoulli, –E uler and – Genocchi polynomials are constructed to show the applications of main results. A further investigation is performed by deriving homogeneous Volterra integral equations for these polynomials and for their relatives. ER -