Voir la notice de l'article provenant de la source Math-Net.Ru
@article{DM_2013_25_4_a7, author = {E. A. Karatsuba}, title = {Fast {Catalan} constant computation via the approximations obtained by the {Kummer's} type transformations}, journal = {Diskretnaya Matematika}, pages = {74--87}, publisher = {mathdoc}, volume = {25}, number = {4}, year = {2013}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/DM_2013_25_4_a7/} }
TY - JOUR AU - E. A. Karatsuba TI - Fast Catalan constant computation via the approximations obtained by the Kummer's type transformations JO - Diskretnaya Matematika PY - 2013 SP - 74 EP - 87 VL - 25 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/DM_2013_25_4_a7/ LA - ru ID - DM_2013_25_4_a7 ER -
E. A. Karatsuba. Fast Catalan constant computation via the approximations obtained by the Kummer's type transformations. Diskretnaya Matematika, Tome 25 (2013) no. 4, pp. 74-87. http://geodesic.mathdoc.fr/item/DM_2013_25_4_a7/
[1] Karatsuba E. A., “Fast computation of some special integrals of mathematical physics”, Sci. Comput., Validated Numerics, Interval Methods, eds. W. Krämer, J. W. von Gudenberg, 2001, 29–41 | DOI | MR
[2] Berndt B. C., Ramanujan's notebooks, v. 1, Springer, 1985 | MR | Zbl
[3] Ramanujan S., Collected papers of Srinivasa Ramanujan, Cambridge University Press, Cambridge, 1927 | Zbl
[4] Karatsuba E. A., “Bystroe vychislenie transtsendentnykh funktsii”, Problemy peredachi informatsii, 27:4 (1991), 76–99 | MR | Zbl
[5] Karatsuba E. A., “Bystroe vychislenie $\zeta(3)$”, Problemy peredachi informatsii, 29:1 (1993), 68–73 | MR | Zbl
[6] Karatsuba Catherine A., “Fast Evaluation of Bessel Functions”, Integral Transforms and Special Functions, 1:4 (1993), 269–276 | DOI | MR | Zbl
[7] Karatsuba E. A., “Bystroe vychislenie dzeta-funktsii Rimana $\zeta(s)$ dlya tselykh znachenii argumenta $s$”, Problemy peredachi informatsii, 31:4 (1995), 69–80 | MR | Zbl
[8] Karatsuba E. A., “Bystroe vychislenie dzeta-funktsii Gurvitsa i $L$-ryadov Dirikhle”, Problemy peredachi informatsii, 34:4 (1998), 62–75 | MR | Zbl
[9] Karatsuba Ekatherine A., “Fast evaluation of hypergeometric function by FEE”, Ser. Approx. Decompos., 11, World Sci., 1999, 303–314 | MR | Zbl
[10] Karatsuba E. A., “On the computation of the Euler constant $\gamma$”, J. Numer. Algor., 24:1–2 (2000), 83–97 | DOI | MR | Zbl
[11] Karatsuba E. A., “Fast computation of $\zeta(3)$ and of some special integrals using the Ramanujan formula and polylogarithms”, BIT Num. Math., 41:4 (2001), 722–730 | DOI | MR | Zbl
[12] Kummer E. E., “Über die Convergenz und Divergenz der unendlichen Reihen”, J. für die reine und angew. Math., 13 (1835), 171–183 | DOI
[13] Kummer E. E., “Eine neue Methode, die numerischen Summen langsam convergirender Reihen zu berechnen”, J. für die reine und angew. Math., 16 (1837), 206–214 | DOI | Zbl
[14] Fikhtengolts G. M., Kurs differentsialnogo i integralnogo ischisleniya, Fizmatgiz, Moskva, 1959
[15] Bailey D. H., Borwein J. M., Mattingly A., Wightwick G., “The computation of previously inaccessible digits of $\pi^2$ and Catalan's constant”, Notices of AMS, 50 (2013), 844–854 | DOI | MR
[16] Catalan E., “Memoire sur la transformation des series et sur quelques integrales defines”, Mem. Acad. Roy. Belgique, 33 (1865), 1–50
[17] Karacuba A., “Berechnungen und die Kompliziertheit von Beziehungen”, EIK, 11 (1975), 10–12
[18] Karatsuba A. A., “Slozhnost vychislenii”, Trudy Matematicheskogo instituta im. V. A. Steklova, 211, 1995, 186–202 | MR | Zbl
[19] Karatsuba A., Ofman Yu., “Umnozhenie mnogoznachnykh chisel na avtomatakh”, Doklady AN SSSR, 145:2 (1962), 293–294
[20] Toom A. L., “O slozhnosti skhemy iz funktsionalnykh elementov, realizuyuschei umnozhenie tselykh chisel”, Doklady AN SSSR, 150:2 (1963), 496–498 | MR | Zbl
[21] Karatsuba A. A., “Kommentarii k moim rabotam, napisannye mnoi samim”, Sovr. probl. matem., 17, MIAN, Moskva, 2013, 7–29 | DOI
[22] Schönhage A., Strassen V., “Schnelle Multiplikation großer Zahlen”, Comput., 7 (1971), 281–292 | DOI | MR | Zbl
[23] Fürer M., “Faster integer multiplication”, SIAM J. Comp., 39:3 (2009), 979–1005 | DOI | MR | Zbl