Dickson Polynomial

A Dickson Polynomial is a Polynomial Sequence that was introduced by L. E. Dickson.

• AKA: Brewer Polynomials.
• Example(s):
  • …
• Counter-Example(s):
  • Cayley Polynomials,
  • Legendre Polynomials,
  • Hermite Polynomials,
  • Romanovski Polynomials.
• See: Transliteration, Orthogonal Functions, Chebyshev Equation, Sturm-Liouville Problem, Chebyshev Nodes, Polynomial Interpolation, Chebyshev Differential Equation, Chebyshev Integral, Chebyshev's Theorem, Chebyshev Function, Permutation, Mathematics, Brewer Sum, Finite Fields, Permutation Polynomial.

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References

2021

• (Wikipedia, 2021) ⇒ https://en.wikipedia.org/wiki/Dickson_polynomial Retrieved:2021-9-12.
  • In mathematics, the Dickson polynomials, denoted D_n(x,α), form a polynomial sequence introduced by L. E. Dickson. They were rediscovered by in his study of Brewer sums and have at times, although rarely, been referred to as Brewer polynomials.

    Over the complex numbers, Dickson polynomials are essentially equivalent to Chebyshev polynomials with a change of variable, and, in fact, Dickson polynomials are sometimes called Chebyshev polynomials.

    Dickson polynomials are generally studied over finite fields, where they sometimes may not be equivalent to Chebyshev polynomials. One of the main reasons for interest in them is that for fixed α, they give many examples of permutation polynomials; polynomials acting as permutations of finite fields.

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