Geodesic
Calculation of hypergeometric series with quasi-linear time and linear space complexity
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 3 (2011), pp. 149-156.

Voir la notice de l'article provenant de la source Math-Net.Ru

A simple for practical implementation algorithm with the time complexity ${\mathsf O}(M(n)\log(n)^2)$ and space complexity ${\mathsf O}(n)$ for the evaluation of hypergeometric series with rational coefficients on the Schönhage machine is constructed (here $M(n)$ is the complexity of integer multiplication). It is shown that this algorithm is suitable in practical informatics for constructive analogues of often used constants of analysis.
Keywords: constructive real numbers, hypergeometric series, quasi-linear time, linear space complexity. 
@article{VSGTU_2011_3_a15,
     author = {S. V. Yakhontov},
     title = {Calculation of hypergeometric series with quasi-linear time and linear space complexity},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {149--156},
     publisher = {mathdoc},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2011_3_a15/}
}
TY  - JOUR
AU  - S. V. Yakhontov
TI  - Calculation of hypergeometric series with quasi-linear time and linear space complexity
JO  - Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
PY  - 2011
SP  - 149
EP  - 156
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VSGTU_2011_3_a15/
LA  - ru
ID  - VSGTU_2011_3_a15
ER  - 
%0 Journal Article
%A S. V. Yakhontov
%T Calculation of hypergeometric series with quasi-linear time and linear space complexity
%J Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
%D 2011
%P 149-156
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VSGTU_2011_3_a15/
%G ru
%F VSGTU_2011_3_a15
S. V. Yakhontov. Calculation of hypergeometric series with quasi-linear time and linear space complexity. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 3 (2011), pp. 149-156. http://geodesic.mathdoc.fr/item/VSGTU_2011_3_a15/

[1] Schönhage A., Grotefeld A. F. W, Vetter E., Fast algorithms. A multitape Turing machine implementation, BI-Wissenschaftsverlag, Mannheim, Germany, 1994, 298 pp. | MR | Zbl

[2] Haible B., Papanikolaou T., “Fast multiprecision evaluation of series of rational numbers”, Algorithmic number theory, 3rd international symposium, ANTS-III, Portland, OR, USA, June 21–25, 1998. Proceedings, Lect. Notes Comput. Sci., 1423, Springer, Berlin, 1998, 338–350 | DOI | MR | Zbl

[3] Cheng H., Gergel B., Kim E., Zima E., “Space-efficient evaluation of hypergeometric series”, SIGSAM Bull., 39:2 (2005), 41–52 | DOI | MR

[4] Yakhontov S. V., $FLINSPACE$ konstruktivnye veschestvennye chisla i funktsii, LAMBERT Academic Publishing, Saarbrucken, 2010, 167 pp.

[5] Gourdon X., Sebah P., Binary splitting method, http://numbers.computation.free.fr/ Constants/Algorithms/splitting.ps

[6] Ko K.-I, Complexity theory of real functions. Progress in Theoretical Computer Science., Birkhäuser Boston, Inc., Boston, MA, 1991, 310 pp. | MR