Polynomial Functions

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Polynomial Functions Support

The Fractal Science Kit fractal generator Polynomial functions support several polynomial functions defined by a recurrence relation.

Complex Polynomial.Evaluate(type, n, k, z)
Complex Polynomial.EvaluateDerivative(type, n, k, z)

The 1st argument specifies the type of polynomial function to use. The 2nd argument to the function, n, is the degree of the recurrence and should be a positive integer. The last argument, z, is the polynomial function variable and is complex. For those types that support an additional argument (LegendreA, LaguerreA, Gegenbauer), the 2nd argument, k, is an additional complex value used by the function. Polynomial.Evaluate returns the value of the function given by type at the complex value z and Polynomial.EvaluateDerivative returns the value of the derivative.

The types are given by the PolynomialTypes enum defined in the built-in macros:

#define PolynomialTypes

enum PolynomialTypes {
  Fibonacci,     "Fibonacci"
  Lucas,         "Lucas"
  Pell,          "Pell"
  PellLucas,     "PellLucas"
  Fermat,        "Fermat"
  FermatLucas,   "FermatLucas"
  Chebyshev1,    "Chebyshev1"
  Chebyshev2,    "Chebyshev2"
  Hermite,       "Hermite"
  Legendre,      "Legendre"
  Laguerre,      "Laguerre"
  LegendreA,     "LegendreA"
  LaguerreA,     "LaguerreA"
  Gegenbauer,    "Gegenbauer"
}
#end

These functions are described in great detail in the Wolfram Web Resource listed below.

Eric W. Weisstein. "Fibonacci Polynomial."

From MathWorld--A Wolfram Web Resource.

 

Eric W. Weisstein. "Lucas Polynomial."

From MathWorld--A Wolfram Web Resource.

 

Eric W. Weisstein. "Pell Polynomial."

From MathWorld--A Wolfram Web Resource.

 

Eric W. Weisstein. "Pell-Lucas Polynomial."

From MathWorld--A Wolfram Web Resource.

 

Eric W. Weisstein. "Fermat Polynomial."

From MathWorld--A Wolfram Web Resource.

 

Eric W. Weisstein. "Fermat-Lucas Polynomial."

From MathWorld--A Wolfram Web Resource.

 

Eric W. Weisstein. "Chebyshev Polynomial of the First Kind."

From MathWorld--A Wolfram Web Resource.

 

Eric W. Weisstein. "Chebyshev Polynomial of the Second Kind."

From MathWorld--A Wolfram Web Resource.

 

Eric W. Weisstein. "Hermite Polynomial."

From MathWorld--A Wolfram Web Resource.

 

Eric W. Weisstein. "Legendre Polynomial."

From MathWorld--A Wolfram Web Resource.

 

Eric W. Weisstein. "Laguerre Polynomial."

From MathWorld--A Wolfram Web Resource.

 

Eric W. Weisstein. "Legendre Polynomial."

From MathWorld--A Wolfram Web Resource.

 

Eric W. Weisstein. "Laguerre Polynomial."

From MathWorld--A Wolfram Web Resource.

 

Eric W. Weisstein. "Gegenbauer Polynomial."

From MathWorld--A Wolfram Web Resource.

 

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