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Differential and integral equations associated with some hybrid families of Legendre polynomials. (English) Zbl 07172256
Summary: The article aims to explore some new classes of differential and integral equations for some hybrid families of Legendre polynomials. Beginning with the recurrence relations and shift operators, the authors derived the differential, integro-differential and partial differential equations for the hybrid Legendre-Appell polynomials. Certain examples are framed for the hybrid Legendre-Bernoulli, Legendre-Euler and Legendre-Genocchi polynomials to show the applications of main results. Further, the homogeneous Volterra integral equations for the hybrid Legendre-Appell and other hybrid families of special polynomials are derived. The inclusion of integral equations is a bonus to this article.

MSC:
 65R20 Numerical methods for integral equations 45J05 Integro-ordinary differential equations 65Q30 Numerical aspects of recurrence relations
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