Apéry's constant (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Apéry's constant" in English language version.

refsWebsite

Global rank English rank

10doi.org

2^nd place

6arxiv.org

69^th place

59^th place

4semanticscholar.org

11^th place

8^th place

4harvard.edu

18^th place

17^th place

3gutenberg.org

489^th place

377^th place

3combinatorics.org

low place

3numberworld.org

low place

2web.archive.org

1^st place

2rutgers.edu

1,999^th place

1,355^th place

2wolfram.com

513^th place

537^th place

1ams.org

451^st place

277^th place

1books.google.com

3^rd place

1numdam.org

8,650^th place

7,668^th place

1mq.edu.au

low place

7,448^th place

1dartmouth.edu

2,242^nd place

1,513^th place

1ntu.edu.tw

2,798^th place

4,271^st place

1worldcat.org

5^th place

1plouffe.fr

low place

1colgate.edu

low place

9,382^nd place

1uqam.ca

8,657^th place

low place

1ucsc.edu

3,619^th place

2,621^st place

1free.fr

321^st place

724^th place

1dipanjan.me

low place

1ehfd.github.io

low place

ams.org

mathscinet.ams.org

Frieze (1985). Frieze, A. M. (1985), "On the value of a random minimum spanning tree problem", Discrete Applied Mathematics, 10 (1): 47–56, doi:10.1016/0166-218X(85)90058-7, MR 0770868.

arxiv.org

Beukers (1979); Zudilin (2002). Beukers, F. (1979), A Note on the Irrationality of $\zeta (2)$ and $\zeta (3)$ , vol. 11, pp. 268–272, doi:10.1112/blms/11.3.268. Zudilin, Wadim (2002), "An elementary proof of Apéry's theorem", arXiv:math/0202159{{cite arXiv}}: CS1 maint: overridden setting (link).
Rivoal (2000). Rivoal, Tanguy (2000), "La fonction zêta de Riemann prend une infinité de valeurs irrationnelles aux entiers impairs", Comptes Rendus de l'Académie des Sciences, Série I, 331 (4): 267–270, arXiv:math/0008051, Bibcode:2000CRASM.331..267R, doi:10.1016/S0764-4442(00)01624-4, S2CID 119678120.
Amdeberhan & Zeilberger (1997). Amdeberhan, Tewodros; Zeilberger, Doron (1997), "Hypergeometric Series Acceleration Via the WZ method", Electronic Journal of Combinatorics, 4 (2), arXiv:math/9804121, Bibcode:1998math......4121A.
Wedeniwski (1998); Wedeniwski (2001). In his message to Simon Plouffe, Sebastian Wedeniwski states that he derived this formula from Amdeberhan & Zeilberger (1997). The discovery year (1998) is mentioned in Simon Plouffe's Table of Records (8 April 2001). Wedeniwski, Sebastian (13 December 1998), The Value of Zeta(3) to 1,000,000 places (Message to Simon Plouffe, with original text but only some decimal places). Wedeniwski, Sebastian (2001), Simon Plouffe (ed.), The Value of Zeta(3) to 1,000,000 places, Project Gutenberg (Message to Simon Plouffe, with all decimal places but a shorter text edited by Simon Plouffe). Amdeberhan, Tewodros; Zeilberger, Doron (1997), "Hypergeometric Series Acceleration Via the WZ method", Electronic Journal of Combinatorics, 4 (2), arXiv:math/9804121, Bibcode:1998math......4121A.
Broadhurst (1998). Broadhurst, D.J. (1998), "Polylogarithmic ladders, hypergeometric series and the ten millionth digits of $\zeta (3)$ and $\zeta (5)$ ", arXiv:math.CA/9803067{{cite arXiv}}: CS1 maint: overridden setting (link).
Tóth, László (2022), "Linear Combinations of Dirichlet Series Associated with the Thue-Morse Sequence" (PDF), Integers, 22 98, arXiv:2211.13570

books.google.com

Mollin (2009). Mollin, Richard A. (2009), Advanced Number Theory with Applications, Discrete Mathematics and Its Applications, CRC Press, p. 220, ISBN 9781420083293.

colgate.edu

math.colgate.edu

Tóth, László (2022), "Linear Combinations of Dirichlet Series Associated with the Thue-Morse Sequence" (PDF), Integers, 22 98, arXiv:2211.13570

combinatorics.org

Amdeberhan (1996). Amdeberhan, Tewodros (1996), "Faster and faster convergent series for $\zeta (3)$ ", Electronic Journal of Combinatorics, 3 (1), doi:10.37236/1237.
Amdeberhan & Zeilberger (1997). Amdeberhan, Tewodros; Zeilberger, Doron (1997), "Hypergeometric Series Acceleration Via the WZ method", Electronic Journal of Combinatorics, 4 (2), arXiv:math/9804121, Bibcode:1998math......4121A.
Wedeniwski (1998); Wedeniwski (2001). In his message to Simon Plouffe, Sebastian Wedeniwski states that he derived this formula from Amdeberhan & Zeilberger (1997). The discovery year (1998) is mentioned in Simon Plouffe's Table of Records (8 April 2001). Wedeniwski, Sebastian (13 December 1998), The Value of Zeta(3) to 1,000,000 places (Message to Simon Plouffe, with original text but only some decimal places). Wedeniwski, Sebastian (2001), Simon Plouffe (ed.), The Value of Zeta(3) to 1,000,000 places, Project Gutenberg (Message to Simon Plouffe, with all decimal places but a shorter text edited by Simon Plouffe). Amdeberhan, Tewodros; Zeilberger, Doron (1997), "Hypergeometric Series Acceleration Via the WZ method", Electronic Journal of Combinatorics, 4 (2), arXiv:math/9804121, Bibcode:1998math......4121A.

dartmouth.edu

math.dartmouth.edu

Euler (1773). Euler, Leonhard (1773), "Exercitationes analyticae" (PDF), Novi Commentarii Academiae Scientiarum Petropolitanae (in Latin), 17: 173–204, retrieved 2008-05-18.

dipanjan.me

Nag (2015). Nag, Dipanjan (2015), "Calculated Apéry's constant to 400,000,000,000 Digit, A world record", Dipanjan

doi.org

Frieze (1985). Frieze, A. M. (1985), "On the value of a random minimum spanning tree problem", Discrete Applied Mathematics, 10 (1): 47–56, doi:10.1016/0166-218X(85)90058-7, MR 0770868.
van der Poorten (1979). van der Poorten, Alfred (1979), "A proof that Euler missed ... Apéry's proof of the irrationality of $\zeta (3)$ " (PDF), The Mathematical Intelligencer, 1 (4): 195–203, doi:10.1007/BF03028234, S2CID 121589323, archived from the original (PDF) on 2011-07-06.
Beukers (1979); Zudilin (2002). Beukers, F. (1979), A Note on the Irrationality of $\zeta (2)$ and $\zeta (3)$ , vol. 11, pp. 268–272, doi:10.1112/blms/11.3.268. Zudilin, Wadim (2002), "An elementary proof of Apéry's theorem", arXiv:math/0202159{{cite arXiv}}: CS1 maint: overridden setting (link).
Rivoal (2000). Rivoal, Tanguy (2000), "La fonction zêta de Riemann prend une infinité de valeurs irrationnelles aux entiers impairs", Comptes Rendus de l'Académie des Sciences, Série I, 331 (4): 267–270, arXiv:math/0008051, Bibcode:2000CRASM.331..267R, doi:10.1016/S0764-4442(00)01624-4, S2CID 119678120.
Zudilin (2001). Zudilin, Wadim (2001), "One of the numbers $\zeta (5)$ , $\zeta (7)$ , $\zeta (9)$ , $\zeta (11)$ is irrational", Russian Mathematical Surveys, 56 (4): 774–776, Bibcode:2001RuMaS..56..774Z, doi:10.1070/RM2001v056n04ABEH000427, S2CID 250734661.
Srivastava (2000), p. 571 (1.11). Srivastava, H. M. (December 2000), "Some Families of Rapidly Convergent Series Representations for the Zeta Functions" (PDF), Taiwanese Journal of Mathematics, 4 (4): 569–599, doi:10.11650/twjm/1500407293, OCLC 36978119, retrieved 2015-08-22.
Amdeberhan (1996). Amdeberhan, Tewodros (1996), "Faster and faster convergent series for $\zeta (3)$ ", Electronic Journal of Combinatorics, 3 (1), doi:10.37236/1237.
Mohammed (2005). Mohammed, Mohamud (2005), "Infinite families of accelerated series for some classical constants by the Markov-WZ method", Discrete Mathematics & Theoretical Computer Science, 7: 11–24, doi:10.46298/dmtcs.342.
Beukers (1979). Beukers, F. (1979), A Note on the Irrationality of $\zeta (2)$ and $\zeta (3)$ , vol. 11, pp. 268–272, doi:10.1112/blms/11.3.268.
Blagouchine (2014). Blagouchine, Iaroslav V. (2014), "Rediscovery of Malmsten's integrals, their evaluation by contour integration methods and some related results", The Ramanujan Journal, 35 (1): 21–110, doi:10.1007/s11139-013-9528-5, S2CID 120943474.

ehfd.github.io

Apéry's constant world record by Seungmin Kim, 28 July 2020, retrieved July 28, 2020.

free.fr

numbers.computation.free.fr

Gourdon & Sebah (2003). Gourdon, Xavier; Sebah, Pascal (2003), The Apéry's constant: $\zeta (3)$ .

gutenberg.org

Wedeniwski (2001). Wedeniwski, Sebastian (2001), Simon Plouffe (ed.), The Value of Zeta(3) to 1,000,000 places, Project Gutenberg (Message to Simon Plouffe, with all decimal places but a shorter text edited by Simon Plouffe).
Wedeniwski (1998); Wedeniwski (2001). In his message to Simon Plouffe, Sebastian Wedeniwski states that he derived this formula from Amdeberhan & Zeilberger (1997). The discovery year (1998) is mentioned in Simon Plouffe's Table of Records (8 April 2001). Wedeniwski, Sebastian (13 December 1998), The Value of Zeta(3) to 1,000,000 places (Message to Simon Plouffe, with original text but only some decimal places). Wedeniwski, Sebastian (2001), Simon Plouffe (ed.), The Value of Zeta(3) to 1,000,000 places, Project Gutenberg (Message to Simon Plouffe, with all decimal places but a shorter text edited by Simon Plouffe). Amdeberhan, Tewodros; Zeilberger, Doron (1997), "Hypergeometric Series Acceleration Via the WZ method", Electronic Journal of Combinatorics, 4 (2), arXiv:math/9804121, Bibcode:1998math......4121A.
Wedeniwski (1998); Wedeniwski (2001). Wedeniwski, Sebastian (13 December 1998), The Value of Zeta(3) to 1,000,000 places (Message to Simon Plouffe, with original text but only some decimal places). Wedeniwski, Sebastian (2001), Simon Plouffe (ed.), The Value of Zeta(3) to 1,000,000 places, Project Gutenberg (Message to Simon Plouffe, with all decimal places but a shorter text edited by Simon Plouffe).

harvard.edu

ui.adsabs.harvard.edu

Rivoal (2000). Rivoal, Tanguy (2000), "La fonction zêta de Riemann prend une infinité de valeurs irrationnelles aux entiers impairs", Comptes Rendus de l'Académie des Sciences, Série I, 331 (4): 267–270, arXiv:math/0008051, Bibcode:2000CRASM.331..267R, doi:10.1016/S0764-4442(00)01624-4, S2CID 119678120.
Zudilin (2001). Zudilin, Wadim (2001), "One of the numbers $\zeta (5)$ , $\zeta (7)$ , $\zeta (9)$ , $\zeta (11)$ is irrational", Russian Mathematical Surveys, 56 (4): 774–776, Bibcode:2001RuMaS..56..774Z, doi:10.1070/RM2001v056n04ABEH000427, S2CID 250734661.
Amdeberhan & Zeilberger (1997). Amdeberhan, Tewodros; Zeilberger, Doron (1997), "Hypergeometric Series Acceleration Via the WZ method", Electronic Journal of Combinatorics, 4 (2), arXiv:math/9804121, Bibcode:1998math......4121A.
Wedeniwski (1998); Wedeniwski (2001). In his message to Simon Plouffe, Sebastian Wedeniwski states that he derived this formula from Amdeberhan & Zeilberger (1997). The discovery year (1998) is mentioned in Simon Plouffe's Table of Records (8 April 2001). Wedeniwski, Sebastian (13 December 1998), The Value of Zeta(3) to 1,000,000 places (Message to Simon Plouffe, with original text but only some decimal places). Wedeniwski, Sebastian (2001), Simon Plouffe (ed.), The Value of Zeta(3) to 1,000,000 places, Project Gutenberg (Message to Simon Plouffe, with all decimal places but a shorter text edited by Simon Plouffe). Amdeberhan, Tewodros; Zeilberger, Doron (1997), "Hypergeometric Series Acceleration Via the WZ method", Electronic Journal of Combinatorics, 4 (2), arXiv:math/9804121, Bibcode:1998math......4121A.

mq.edu.au

maths.mq.edu.au

van der Poorten (1979). van der Poorten, Alfred (1979), "A proof that Euler missed ... Apéry's proof of the irrationality of $\zeta (3)$ " (PDF), The Mathematical Intelligencer, 1 (4): 195–203, doi:10.1007/BF03028234, S2CID 121589323, archived from the original (PDF) on 2011-07-06.

ntu.edu.tw

society.math.ntu.edu.tw

Srivastava (2000), p. 571 (1.11). Srivastava, H. M. (December 2000), "Some Families of Rapidly Convergent Series Representations for the Zeta Functions" (PDF), Taiwanese Journal of Mathematics, 4 (4): 569–599, doi:10.11650/twjm/1500407293, OCLC 36978119, retrieved 2015-08-22.

numberworld.org

Yee (2009). Yee, Alexander J. (2009), Large Computations.
Yee (2017). Yee, Alexander J. (2017), Zeta(3) - Apéry's Constant
Yee, Alexander, Records set by y-cruncher, retrieved April 1, 2024.

numdam.org

Apéry (1979). Apéry, Roger (1979), "Irrationalité de $\zeta 2$ et $\zeta 3$ ", Astérisque, 61: 11–13.

plouffe.fr

Wedeniwski (1998); Wedeniwski (2001). In his message to Simon Plouffe, Sebastian Wedeniwski states that he derived this formula from Amdeberhan & Zeilberger (1997). The discovery year (1998) is mentioned in Simon Plouffe's Table of Records (8 April 2001). Wedeniwski, Sebastian (13 December 1998), The Value of Zeta(3) to 1,000,000 places (Message to Simon Plouffe, with original text but only some decimal places). Wedeniwski, Sebastian (2001), Simon Plouffe (ed.), The Value of Zeta(3) to 1,000,000 places, Project Gutenberg (Message to Simon Plouffe, with all decimal places but a shorter text edited by Simon Plouffe). Amdeberhan, Tewodros; Zeilberger, Doron (1997), "Hypergeometric Series Acceleration Via the WZ method", Electronic Journal of Combinatorics, 4 (2), arXiv:math/9804121, Bibcode:1998math......4121A.

rutgers.edu

math.rutgers.edu

Wedeniwski (1998); Wedeniwski (2001). In his message to Simon Plouffe, Sebastian Wedeniwski states that he derived this formula from Amdeberhan & Zeilberger (1997). The discovery year (1998) is mentioned in Simon Plouffe's Table of Records (8 April 2001). Wedeniwski, Sebastian (13 December 1998), The Value of Zeta(3) to 1,000,000 places (Message to Simon Plouffe, with original text but only some decimal places). Wedeniwski, Sebastian (2001), Simon Plouffe (ed.), The Value of Zeta(3) to 1,000,000 places, Project Gutenberg (Message to Simon Plouffe, with all decimal places but a shorter text edited by Simon Plouffe). Amdeberhan, Tewodros; Zeilberger, Doron (1997), "Hypergeometric Series Acceleration Via the WZ method", Electronic Journal of Combinatorics, 4 (2), arXiv:math/9804121, Bibcode:1998math......4121A.
Wedeniwski (1998); Wedeniwski (2001). Wedeniwski, Sebastian (13 December 1998), The Value of Zeta(3) to 1,000,000 places (Message to Simon Plouffe, with original text but only some decimal places). Wedeniwski, Sebastian (2001), Simon Plouffe (ed.), The Value of Zeta(3) to 1,000,000 places, Project Gutenberg (Message to Simon Plouffe, with all decimal places but a shorter text edited by Simon Plouffe).

semanticscholar.org

api.semanticscholar.org

van der Poorten (1979). van der Poorten, Alfred (1979), "A proof that Euler missed ... Apéry's proof of the irrationality of $\zeta (3)$ " (PDF), The Mathematical Intelligencer, 1 (4): 195–203, doi:10.1007/BF03028234, S2CID 121589323, archived from the original (PDF) on 2011-07-06.
Rivoal (2000). Rivoal, Tanguy (2000), "La fonction zêta de Riemann prend une infinité de valeurs irrationnelles aux entiers impairs", Comptes Rendus de l'Académie des Sciences, Série I, 331 (4): 267–270, arXiv:math/0008051, Bibcode:2000CRASM.331..267R, doi:10.1016/S0764-4442(00)01624-4, S2CID 119678120.
Zudilin (2001). Zudilin, Wadim (2001), "One of the numbers $\zeta (5)$ , $\zeta (7)$ , $\zeta (9)$ , $\zeta (11)$ is irrational", Russian Mathematical Surveys, 56 (4): 774–776, Bibcode:2001RuMaS..56..774Z, doi:10.1070/RM2001v056n04ABEH000427, S2CID 250734661.
Blagouchine (2014). Blagouchine, Iaroslav V. (2014), "Rediscovery of Malmsten's integrals, their evaluation by contour integration methods and some related results", The Ramanujan Journal, 35 (1): 21–110, doi:10.1007/s11139-013-9528-5, S2CID 120943474.

ucsc.edu

scipp.ucsc.edu

Haber, Howard E. (Winter 2010), "The logarithmic derivative of the Gamma function" (PDF), Physics 116A lecture notes, University of California, Santa Cruz

uqam.ca

lacim.uqam.ca

Plouffe (1998). Plouffe, Simon (1998), Identities inspired from Ramanujan Notebooks II, archived from the original on 2002-12-14.

web.archive.org

van der Poorten (1979). van der Poorten, Alfred (1979), "A proof that Euler missed ... Apéry's proof of the irrationality of $\zeta (3)$ " (PDF), The Mathematical Intelligencer, 1 (4): 195–203, doi:10.1007/BF03028234, S2CID 121589323, archived from the original (PDF) on 2011-07-06.
Plouffe (1998). Plouffe, Simon (1998), Identities inspired from Ramanujan Notebooks II, archived from the original on 2002-12-14.

wolfram.com

mathworld.wolfram.com

Weisstein, Eric W., "Apéry's Constant", mathworld.wolfram.com, retrieved 2024-09-21
Weisstein, Eric W., "Apéry's Constant Continued Fraction", mathworld.wolfram.com, retrieved 2024-09-21

worldcat.org

search.worldcat.org

Srivastava (2000), p. 571 (1.11). Srivastava, H. M. (December 2000), "Some Families of Rapidly Convergent Series Representations for the Zeta Functions" (PDF), Taiwanese Journal of Mathematics, 4 (4): 569–599, doi:10.11650/twjm/1500407293, OCLC 36978119, retrieved 2015-08-22.