Function
NumCosmoMathSpectralchebyshev_deriv
Declaration [src]
gdouble
ncm_spectral_chebyshev_deriv (
GArray* a,
gdouble t
)
Description [src]
Evaluates the first derivative of a Chebyshev expansion at $t$.
The Chebyshev series is $$ f(t) = \sum_{j=0}^{N-1} a_j T_j(t) , $$ and its derivative can be written as $$ f’(t) = \sum_{k=0}^{N-2} b_k T_k(t) . $$
The derivative coefficients $b_k$ satisfy $$ b_k = \sum_{j=k+1,k+3,\dots}^{N-1} 2 j a_j , \quad k \ge 1, $$ and $$ b_0 = \sum_{j=1,3,5,\dots}^{N-1} j a_j . $$
The derivative is evaluated using a fused backward recurrence and the Clenshaw algorithm, without explicitly forming the coefficients $b_k$.