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

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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. 
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     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/}
}
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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/