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A note on Chebyshev polynomials

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Si derivano nuove famiglie di funzioni generatrici e di identità relative ai polinomi di Chebyshev. Si dimostra che il metodo proposto permette la derivazione di regole di somma relative a prodotti di polinomi di Chebyshev e teoremi di addizione. La possibilità di estendere i risultati includendos funzioni generatrici di prodotti di polinomi di Chebyshev ed altri polinomi è infine analizzata.

Abstract

New families of generating functions and identities concerning the Chebyshev polynomials are derived. It is shown that the proposed method allows the derivation of sum rules involving products of Chebyshev polynomials and addition theorems. The possiblity of extending the results to include gnerating functions involving products of Chebyshev and other polynomials is finally analyzed.

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References

  1. L. C. Andrews,Special functions for applied mathematicians and engineers, Mc Millan, New York (1985);L. Gatteschi,Funzioni Speciali, UTET, Torino (1973);T. J. Rivlin,The Chebyshev Polynomials, J. Wiley & Sons, New York (1974).

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  2. G. Dattoli—A Torre,Theory and applications of generalized Bessel functions, Aracne (Rome) (1996).

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Author notes

  1. G. Dattoli

    Present address: Dipartimento Innovazione Divisione Fisica Applicata C.R. Frascati, Via Enrico Fermi 45, 00044, Frascati, Rome, Italy

  2. D. Sacchetti

    Present address: Dipartimento di Statistica, Probabilità e Stat. Appl., Università Egli Studi «La Sapienza», Piazzale Aldo Moro 5, 00185, Rome, Italy

  3. C. Cesarano

    Present address: , Via G. Carducci 2, Roma

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    1. G. Dattoli
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    2. D. Sacchetti
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    3. C. Cesarano
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    Dattoli, G., Sacchetti, D. & Cesarano, C. A note on Chebyshev polynomials. Ann. Univ. Ferrara 47, 107–115 (2001). https://doi.org/10.1007/BF02838178

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    • DOI: https://doi.org/10.1007/BF02838178

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