math-functions-0.1.1.1: Special functions and Chebyshev polynomials

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Numeric.Polynomial.Chebyshev

Contents

Description

Chebyshev polynomials.

Synopsis

# Chebyshev polinomials

A Chebyshev polynomial of the first kind is defined by the following recurrence:

``` t 0 _ = 1
t 1 x = x
t n x = 2 * x * t (n-1) x - t (n-2) x
```

Arguments

 :: Vector v Double => Double Parameter of each function. -> v Double Coefficients of each polynomial term, in increasing order. -> Double

Evaluate a Chebyshev polynomial of the first kind. Uses Clenshaw's algorithm.

Arguments

 :: Vector v Double => Double Parameter of each function. -> v Double Coefficients of each polynomial term, in increasing order. -> Double

Evaluate a Chebyshev polynomial of the first kind. Uses Broucke's ECHEB algorithm, and his convention for coefficient handling, and so gives different results than `chebyshev` for the same inputs.

# References

• Broucke, R. (1973) Algorithm 446: Ten subroutines for the manipulation of Chebyshev series. Communications of the ACM 16(4):254–256. http://doi.acm.org/10.1145/362003.362037
• Clenshaw, C.W. (1962) Chebyshev series for mathematical functions. National Physical Laboratory Mathematical Tables 5, Her Majesty's Stationery Office, London.