We study a hybrid family of three-variable Legendre–Laguerre–Appell polynomials and establish their properties, including the series expansions, determinant forms, recurrence relations, and shift operators, followed by differential, integrodifferential and partial differential equations. Similar results are deduced for the three-variable Hermite–Laguerre–Appell polynomials. Some examples are constructed in terms of the Legendre–Laguerre–Bernoulli, –Euler, and –Genocchi polynomials in oder to show the applications of the main results. We also deduce homogeneous Volterra integral equations for these polynomials and their relatives.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, No. 3, pp. 408–424, March, 2021. Ukrainian DOI: 10.37863/umzh.v73i3.894.
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Khan, S., Riyasat, M. & Wani, S.A. Differential and Integral Equations for Legendre–Laguerre-Based Hybrid Polynomials. Ukr Math J 73, 479–497 (2021). https://doi.org/10.1007/s11253-021-01937-8
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DOI: https://doi.org/10.1007/s11253-021-01937-8