Clenshaw%E2%80%93Curtis%20formula%20%28extended%29
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1: Bibliography C
2: Bibliography P
3: 29.20 Methods of Computation
4: Bibliography O
5: 3.5 Quadrature
6: 18.40 Methods of Computation
7: 28.34 Methods of Computation
Solution of the systems of linear algebraic equations (28.4.5)–(28.4.8) and (28.14.4), with the conditions (28.4.9)–(28.4.12) and (28.14.5), by boundary-value methods (§3.6) to determine the Fourier coefficients. Subsequently, the Fourier series can be summed with the aid of Clenshaw’s algorithm (§3.11(ii)). See Meixner and Schäfke (1954, §2.87). This procedure can be combined with §28.34(ii)(d).
8: Bibliography T
9: 6.20 Approximations
Cody and Thacher (1968) provides minimax rational approximations for , with accuracies up to 20S.
Cody and Thacher (1969) provides minimax rational approximations for , with accuracies up to 20S.
MacLeod (1996b) provides rational approximations for the sine and cosine integrals and for the auxiliary functions and , with accuracies up to 20S.
Clenshaw (1962) gives Chebyshev coefficients for for and for (20D).