Fast Computation of Singular Oscillatory Fourier Transforms

Table 5

Absolute errors in 𝑛-point approximations by the proposed method to the integral ∫¹₋₁(𝑥+1)^−(1/2)(1−𝑥)^−(1/2)𝑒^𝑥𝑒^𝑖𝜔𝑥𝑑𝑥.

𝜔⧵𝑛	2	3	4
5	1.1×10^−4	3.5×10^−6	2.0×10^−7
10	7.3×10^−6	5.0×10^−8	1.0×10^−9
20	3.4×10^−7	7.2×10^−10	4.2×10^−12
40	1.5×10^−9	5.3×10^−12	9.5×10^−15