Fast Multiprecision Evaluation of Series of Rational Numbers

We describe two techniques for fast multiple-precision evaluation of linearly convergent series, including power series and Ramanujan series. The computation time for N bits is O((log N)2 M(N)), where M(N) is the time needed to multiply two N-bit numbers. Applications include fast algorithms for elementary functions, , hypergeometric functions at rational points, (3), Euler's, Catalan's and Ap

• Type: Conference
• Year: 1998
• Where: ANTS
• Authors: Bruno Haible, Thomas Papanikolaou
• Keywords: Algorithms, ANTS 1998, Convergent Series, Fast Multiple-precision Evaluation, Ramanujan Series