Сумма обратных квадратов
Matematicheskoe Prosveshchenie, Matematicheskoe Prosveshchenie (2004), pp. 142-163.

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

@article{MP_2004_a13,
     author = {K. P. Kokhas'},
     title = {{\CYRS}{\cyru}{\cyrm}{\cyrm}{\cyra} {\cyro}{\cyrb}{\cyrr}{\cyra}{\cyrt}{\cyrn}{\cyrery}{\cyrh} {\cyrk}{\cyrv}{\cyra}{\cyrd}{\cyrr}{\cyra}{\cyrt}{\cyro}{\cyrv}},
     journal = {Matematicheskoe Prosveshchenie},
     pages = {142--163},
     publisher = {mathdoc},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MP_2004_a13/}
}
TY  - JOUR
AU  - K. P. Kokhas'
TI  - Сумма обратных квадратов
JO  - Matematicheskoe Prosveshchenie
PY  - 2004
SP  - 142
EP  - 163
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MP_2004_a13/
LA  - ru
ID  - MP_2004_a13
ER  - 
%0 Journal Article
%A K. P. Kokhas'
%T Сумма обратных квадратов
%J Matematicheskoe Prosveshchenie
%D 2004
%P 142-163
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MP_2004_a13/
%G ru
%F MP_2004_a13
K. P. Kokhas'. Сумма обратных квадратов. Matematicheskoe Prosveshchenie, Matematicheskoe Prosveshchenie (2004), pp. 142-163. http://geodesic.mathdoc.fr/item/MP_2004_a13/

[1] Aierlend K., Rouzen M., Klassicheskoe vvedenie v sovremennuyu teoriyu chisel, Mir, M., 1987

[2] Evgrafov M. A., Asimptoticheskie otsenki i tselye funktsii, Nauka, M., 1979

[3] Makarov B. M., Goluzina M. G., Lodkin A. A., Podkorytov A. N., Izbrannye zadachi po veschestvennomu analizu, Nauka, M., 1992

[4] Poia D., Matematika i pravdopodobnye rassuzhdeniya, Nauka, M., 1975

[5] Titchmarsh E., Teoriya funktsii, Nauka, M., 1980

[6] Titchmarsh E., Vvedenie v teoriyu integralov Fure, Gostekhizdat, M.-L., 1948

[7] Uitteker E. T., Vatson Dzh. N., Kurs sovremennogo analiza, Chast vtoraya, Fizmatlit, M., 1963

[8] Fikhtengolts G. M., Kurs differentsialnogo i integralnogo ischisleniya, T. 2, Nevskii Dialekt, SPb, 2002

[9] Khardi G., Raskhodyaschiesya ryady, IL, M., 1951

[10] Yaglom A. M., Yaglom I. M., Neelementarnye zadachi v elementarnom izlozhenii, GITTL, M., 1954

[11] Apostol T. M., “A proof that Eider missid: evaluting $\zeta(2)$”, Math. Intel., 60 (1983) | MR | Zbl

[12] Chapman R., Evaluating $\zeta(2)$, http://www.maths.ex.ac.uk/~rjc/rjc.html

[13] Elkies N., On the sums $\sum\limits_{k=-\infty}^{+\infty}\frac1{(2k+1)^{-n}}$, arxiv.org/math.CA/0101168

[14] Kortram R. A., “Simple proofs for $\sum\limits_{k=1}^\infty\frac1{k^2}=\frac{\pi^2}6$ and $\sin x=x\prod\limits_{k=1}^\infty(1-\frac{x^2}{\pi^2k^2})$”, Math. Mag., 69 (1996), 122–125 | Zbl

[15] Matsuoka Y., “An elementary proof of the formula $\sum\limits_{k=1}^\infty\frac1{k^2}=\frac{\pi^2}6$”, Amer. Math. Monthly, 68 (1961), 486–487 | MR

[16] Russel D., “Another Eulerian-type proof”, Math. Mag., 60 (1991), 349

[17] Stark E. L., “The series $\sum\limits_{k=1}^\infty k^{-s}$, $s=2,3,4,\dots$, once more”, Math. Mag., 47 (1974), 197–202 | MR | Zbl

[18] {\tt newsgroup: sci.math.research}