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

9doi.org

2^nd place

8arxiv.org

69^th place

59^th place

4harvard.edu

18^th place

17^th place

3gutenberg.org

489^th place

377^th place

3semanticscholar.org

11^th place

8^th place

3combinatorics.org

low place

3numberworld.org

low 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

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

1web.archive.org

1^st 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 (Global: 451^st place; English: 277^th place)

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 (Global: 69^th place; English: 59^th place)

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 (1996). Amdeberhan, Tewodros (1996), "Faster and faster convergent series for $\zeta (3)$ ", Electronic Journal of Combinatorics, 3 (1), arXiv:math/9804126, 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.
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).
S. N. Gladkovskii An elementary derivation of the formula of Yu.V. Nesterenko expansion in continued fraction of a number 2*ζ(3) https://arxiv.org/pdf/2411.07513
Gutnik L.A. On the number ζ(3). https://arxiv.org/pdf/0902.4732.pdf.}}

books.google.com (Global: 3^rd place; English: 3^rd place)

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

combinatorics.org (Global: low place; English: low place)

Amdeberhan (1996). Amdeberhan, Tewodros (1996), "Faster and faster convergent series for $\zeta (3)$ ", Electronic Journal of Combinatorics, 3 (1), arXiv:math/9804126, 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 (Global: 2,242^nd place; English: 1,513^th place)

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 (Global: low place; English: low place)

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

doi.org (Global: 2^nd place; English: 2^nd place)

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.
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), arXiv:math/9804126, 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, 7 342: 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 (Global: low place; English: low place)

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

free.fr (Global: 321^st place; English: 724^th place)

numbers.computation.free.fr

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

gutenberg.org (Global: 489^th place; English: 377^th place)

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 (Global: 18^th place; English: 17^th place)

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.

ntu.edu.tw (Global: 2,798^th place; English: 4,271^st place)

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 (Global: low place; English: low place)

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 (Global: 8,650^th place; English: 7,668^th place)

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

plouffe.fr (Global: low place; English: low place)

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 (Global: 1,999^th place; English: 1,355^th place)

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 (Global: 11^th place; English: 8^th place)

api.semanticscholar.org

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 (Global: 3,619^th place; English: 2,621^st place)

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 (Global: 8,657^th place; English: low place)

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 (Global: 1^st place; English: 1^st place)

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

wolfram.com (Global: 513^th place; English: 537^th place)

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 (Global: 5^th place; English: 5^th place)

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.

Apéry's constant (English Wikipedia)

ams.org (Global: 451st place; English: 277th place)

mathscinet.ams.org

arxiv.org (Global: 69th place; English: 59th place)

books.google.com (Global: 3rd place; English: 3rd place)

combinatorics.org (Global: low place; English: low place)

dartmouth.edu (Global: 2,242nd place; English: 1,513th place)

math.dartmouth.edu

dipanjan.me (Global: low place; English: low place)

doi.org (Global: 2nd place; English: 2nd place)

ehfd.github.io (Global: low place; English: low place)

free.fr (Global: 321st place; English: 724th place)

numbers.computation.free.fr

gutenberg.org (Global: 489th place; English: 377th place)

harvard.edu (Global: 18th place; English: 17th place)

ui.adsabs.harvard.edu

ntu.edu.tw (Global: 2,798th place; English: 4,271st place)

society.math.ntu.edu.tw

numberworld.org (Global: low place; English: low place)

numdam.org (Global: 8,650th place; English: 7,668th place)

plouffe.fr (Global: low place; English: low place)

rutgers.edu (Global: 1,999th place; English: 1,355th place)

math.rutgers.edu

semanticscholar.org (Global: 11th place; English: 8th place)

api.semanticscholar.org

ucsc.edu (Global: 3,619th place; English: 2,621st place)

scipp.ucsc.edu

uqam.ca (Global: 8,657th place; English: low place)

lacim.uqam.ca

web.archive.org (Global: 1st place; English: 1st place)

wolfram.com (Global: 513th place; English: 537th place)

mathworld.wolfram.com

worldcat.org (Global: 5th place; English: 5th place)

search.worldcat.org

ams.org (Global: 451^st place; English: 277^th place)

arxiv.org (Global: 69^th place; English: 59^th place)

books.google.com (Global: 3^rd place; English: 3^rd place)

dartmouth.edu (Global: 2,242^nd place; English: 1,513^th place)

doi.org (Global: 2^nd place; English: 2^nd place)

free.fr (Global: 321^st place; English: 724^th place)

gutenberg.org (Global: 489^th place; English: 377^th place)

harvard.edu (Global: 18^th place; English: 17^th place)

ntu.edu.tw (Global: 2,798^th place; English: 4,271^st place)

numdam.org (Global: 8,650^th place; English: 7,668^th place)

rutgers.edu (Global: 1,999^th place; English: 1,355^th place)

semanticscholar.org (Global: 11^th place; English: 8^th place)

ucsc.edu (Global: 3,619^th place; English: 2,621^st place)

uqam.ca (Global: 8,657^th place; English: low place)

web.archive.org (Global: 1^st place; English: 1^st place)

wolfram.com (Global: 513^th place; English: 537^th place)

worldcat.org (Global: 5^th place; English: 5^th place)