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A note on Legendre polynomials. (English) Zbl 1075.33502
Summary: We use an operational method to show that Legendre polynomials can be viewed as discrete convolutions of Laguerre polynomials. It is furthermore shown that they can be derived as the particular case of a new family of two-variable orthogonal polynomials, whose properties are studied with some detail. It is furthermore shown that this point of view allows the derivation of new properties of Legendre polynomials and it is also shown how it can be extended to the Jacobi family.

MSC:
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
33C50 Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable
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[1] DOI: 10.1016/S0377-0427(99)00111-9 · Zbl 0949.33005 · doi:10.1016/S0377-0427(99)00111-9
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