Chebyshev recursion formula

Even for fairly short spectral ranges, the computing time involved for this operation can be quite high, especially if each cosine term required is calculated from a series. Cosine tables can be stored in the computer memory, but this does not provide an adequate solution. It has been found that a successfiil method of circumventing this problem is by the use of recursion relationships, whereby a value for cos 2i6i kh can be calculated from the value of cos 2n ih. In this way, only one cosine value has to be calculated for each spectral wavenumber. The Chebyshev recursion formula. 

The Pn are Chebyshev polynomials of complex argument. They obey the recursion formula... 

The sine values are calculated with the use of another recursion formula also attributed to Chebyshev ... 

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