Journal of Applied Analysis 06 (2000), No. 2, 259--282
Copyright Heldermann Verlag 2000
Integrals of Legendre Polynomials and Solution of Some Partial Differential Equations
Rachel Belinsky
Morris Brown College, Atlanta, GA 30314, U.S.A.
We show a connection between the polynomials whose inflection points coincide with their interior roots (called PIPCIRs), Legendre polynomials, and Jacobi polynomials, and study some properties of PIPCIRs (Part I). In addition, we give new formulas for some classical orthogonal polynomials. Then we use PIPCIRs to solve some partial differential equations (Part II).
Keywords: Orthogonal polynomials, Legendre polynomials, Jacobi polynomials, generating function.
MSC: 42C05; 26C05, 26C10, 26C99
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