Families of Legendre-Sheffer polynomials. (English) Zbl 1255.33004
Summary: We introduce families of Legendre-Sheffer polynomials corresponding to two different forms of 2-variable Legendre polynomials. We discuss their special properties and establish a correspondence between the Sheffer and Legendre-Sheffer families. Further, we obtain some important results involving Legendre-Hermite and Legendre-Laguerre polynomials as applications.
MSC:
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
References:
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