Interpolation of power series uniformly convergent in the unit disk

Acceleration of algebraically-converging

Acceleration of algebraically-converging Fourier series when the coefficients have series in powers of

✍ John P. Boyd 📂 Article 📅 2009 🏛 Elsevier Science 🌐 English ⚖ 250 KB

If the coefficients in a Fourier cosine series, f ðxÞ % f N ¼ P 1 n¼0 a n cosðnxÞ, decrease as a small negative power of n, then one may need millions of terms to sum the series to high accuracy. We show that if the a n are known analytically and have a power series in 1=n, then it is straightforwar