Abstract
In this paper, we shall be concerned with lowering operators defined on polynomials by means of
We determine a necessary and sufficient condition on lowering operators L and a symmetric orthogonal polynomial sets \(\{P_n\}_{n\ge 0}\) such that \(\{P_n\}_{n\ge 0}\) is L-Appell. The resulting polynomials are the generalized Hermite and the symmetric PSs related to Wall and generalized Stieltjes–Wigert. Various properties of the obtained families are singled out: a three-term recurrence relation, explicit expression in term of hypergeometric and basic hypergeometric functions and generating functions.
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Gaied, M. The L-Appell Symmetric Orthogonal Polynomials. Mediterr. J. Math. 14, 211 (2017). https://doi.org/10.1007/s00009-017-1006-7
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DOI: https://doi.org/10.1007/s00009-017-1006-7
Keywords
- Orthogonal polynomials
- symmetric orthogonal polynomials
- L-Appell polynomials
- lowering operators
- generalized Hermite polynomials