Geodesic
On the exponential integral computation
Matematičeskoe modelirovanie, Tome 20 (2008) no. 1, pp. 87-91 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

New high-precision algorithm for exponential integral calculation was developed. It is based on the representation of exponential integral in form of convergent series when $x$-argument is not large and in form of asymptotically convergent continued fraction when $x$ is large. It was shown that the optimal bound between these representations is $x=1$. At the same time using of 18 series members and 220 continued fraction members guarantees relative pre-cision lower than $2\cdot 10^{-15}$, that exceeds practical needs. 
@article{MM_2008_20_1_a6,
     author = {N. N. Kalitkin and I. A. Panin},
     title = {On the exponential integral computation},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {87--91},
     year = {2008},
     volume = {20},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2008_20_1_a6/}
}
TY  - JOUR
AU  - N. N. Kalitkin
AU  - I. A. Panin
TI  - On the exponential integral computation
JO  - Matematičeskoe modelirovanie
PY  - 2008
SP  - 87
EP  - 91
VL  - 20
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MM_2008_20_1_a6/
LA  - ru
ID  - MM_2008_20_1_a6
ER  - 
%0 Journal Article
%A N. N. Kalitkin
%A I. A. Panin
%T On the exponential integral computation
%J Matematičeskoe modelirovanie
%D 2008
%P 87-91
%V 20
%N 1
%U http://geodesic.mathdoc.fr/item/MM_2008_20_1_a6/
%G ru
%F MM_2008_20_1_a6
N. N. Kalitkin; I. A. Panin. On the exponential integral computation. Matematičeskoe modelirovanie, Tome 20 (2008) no. 1, pp. 87-91. http://geodesic.mathdoc.fr/item/MM_2008_20_1_a6/

[1] E. S. Kuznetsov, Izbrannye nauchnye trudy, FIZMATLIT, M., 2003

[2] M. Abramowitz, I. A. Stegun (ed.), Handbook of mathematical functions with formulas, graphs, and mathematical tables, John Wiley Sons, New York, 1972 | MR | Zbl

[3] S. Chepmen, T. Kauling, Matematicheskaya teoriya neodnorodnykh gazov, Izdatelstvo inostrannoi literatury, M., 1960 | MR