Abstract
In this paper, using the Faa di Bruno formula and some properties of the Bell polynomials of the second kind, we obtain a new explicit formula for the generalized Humbert-Hermite polynomials. We provide determinantal representations for the ratio of two differentiable functions. We obtain a recursive relation for the generalized Humbert-Hermite polynomials. As a practice, we derive an alternative recursive relation for generalized Humbert-Hermite polynomials via the Hessenberg determinant. Finally, we derive several families of multilinear and multilateral generating functions for the generalized Humbert-Hermite-type polynomials and other polynomials which are mentioned in this paper. Our results also include many well-known polynomials in the literature.
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Kapsamı
Uluslararası
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Type
Hakemli
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Index info
WOS.SCI
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Language
English
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Article Type
None
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Keywords
Fibonacci polynomials generalized Fibonacci polynomials generating function Hessenberg determinant Humbert-Hermite polynomials recursive relation