Stirling's approximation (English Wikipedia)

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

refsWebsite

Global rank English rank

10doi.org

2^nd place

5semanticscholar.org

11^th place

8^th place

3jstor.org

26^th place

20^th place

3ams.org

451^st place

277^th place

2archive.org

6^th place

2harvard.edu

18^th place

17^th place

2web.archive.org

1^st place

1nist.gov

355^th place

454^th place

1york.ac.uk

7,670^th place

5,196^th place

1rskey.org

low place

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

mathscinet.ams.org

Le Cam, L. (1986), "The central limit theorem around 1935", Statistical Science, 1 (1): 78–96, doi:10.1214/ss/1177013818, JSTOR 2245503, MR 0833276; see p. 81, "The result, obtained using a formula originally proved by de Moivre but now called Stirling's formula, occurs in his 'Doctrine of Chances' of 1733."
Flajolet, Philippe; Sedgewick, Robert (2009), Analytic Combinatorics, Cambridge, UK: Cambridge University Press, p. 555, doi:10.1017/CBO9780511801655, ISBN 978-0-521-89806-5, MR 2483235, S2CID 27509971
Karatsuba, Ekatherina A. (2001), "On the asymptotic representation of the Euler gamma function by Ramanujan", Journal of Computational and Applied Mathematics, 135 (2): 225–240, Bibcode:2001JCoAM.135..225K, doi:10.1016/S0377-0427(00)00586-0, MR 1850542

archive.org (Global: 6^th place; English: 6^th place)

Methodus Differentialis: Sive Tractatus de Summatione et Interpolatione Serierum Infinitarum, Jacob Stirling, London, 1730
Ramanujan, Srinivasa (14 August 1920), Lost Notebook and Other Unpublished Papers, p. 339 – via Internet Archive

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

Dutka, Jacques (1991), "The early history of the factorial function", Archive for History of Exact Sciences, 43 (3): 225–249, doi:10.1007/BF00389433, S2CID 122237769
Le Cam, L. (1986), "The central limit theorem around 1935", Statistical Science, 1 (1): 78–96, doi:10.1214/ss/1177013818, JSTOR 2245503, MR 0833276; see p. 81, "The result, obtained using a formula originally proved by de Moivre but now called Stirling's formula, occurs in his 'Doctrine of Chances' of 1733."
Pearson, Karl (1924), "Historical note on the origin of the normal curve of errors", Biometrika, 16 (3/4): 402–404 [p. 403], doi:10.2307/2331714, JSTOR 2331714, I consider that the fact that Stirling showed that De Moivre's arithmetical constant was ${\sqrt {2\pi }}$ does not entitle him to claim the theorem, [...]
Flajolet, Philippe; Sedgewick, Robert (2009), Analytic Combinatorics, Cambridge, UK: Cambridge University Press, p. 555, doi:10.1017/CBO9780511801655, ISBN 978-0-521-89806-5, MR 2483235, S2CID 27509971
Robbins, Herbert (1955), "A Remark on Stirling's Formula", The American Mathematical Monthly, 62 (1): 26–29, doi:10.2307/2308012, JSTOR 2308012
Nemes, Gergő (2010), "New asymptotic expansion for the Gamma function", Archiv der Mathematik, 95 (2): 161–169, doi:10.1007/s00013-010-0146-9, S2CID 121820640
Karatsuba, Ekatherina A. (2001), "On the asymptotic representation of the Euler gamma function by Ramanujan", Journal of Computational and Applied Mathematics, 135 (2): 225–240, Bibcode:2001JCoAM.135..225K, doi:10.1016/S0377-0427(00)00586-0, MR 1850542
Mortici, Cristinel (2011), "Ramanujan's estimate for the gamma function via monotonicity arguments", Ramanujan J., 25 (2): 149–154, doi:10.1007/s11139-010-9265-y, S2CID 119530041
Mortici, Cristinel (2011), "Improved asymptotic formulas for the gamma function", Comput. Math. Appl., 61 (11): 3364–3369, doi:10.1016/j.camwa.2011.04.036.
Mortici, Cristinel (2011), "On Ramanujan's large argument formula for the gamma function", Ramanujan J., 26 (2): 185–192, doi:10.1007/s11139-010-9281-y, S2CID 120371952.

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

ui.adsabs.harvard.edu

Bayes, Thomas (24 November 1763), "A letter from the late Reverend Mr. Thomas Bayes, F. R. S. to John Canton, M. A. and F. R. S." (PDF), Philosophical Transactions, 53: 269, Bibcode:1763RSPT...53..269B, archived (PDF) from the original on 2012-01-28, retrieved 2012-03-01
Karatsuba, Ekatherina A. (2001), "On the asymptotic representation of the Euler gamma function by Ramanujan", Journal of Computational and Applied Mathematics, 135 (2): 225–240, Bibcode:2001JCoAM.135..225K, doi:10.1016/S0377-0427(00)00586-0, MR 1850542

jstor.org (Global: 26^th place; English: 20^th place)

Le Cam, L. (1986), "The central limit theorem around 1935", Statistical Science, 1 (1): 78–96, doi:10.1214/ss/1177013818, JSTOR 2245503, MR 0833276; see p. 81, "The result, obtained using a formula originally proved by de Moivre but now called Stirling's formula, occurs in his 'Doctrine of Chances' of 1733."
Pearson, Karl (1924), "Historical note on the origin of the normal curve of errors", Biometrika, 16 (3/4): 402–404 [p. 403], doi:10.2307/2331714, JSTOR 2331714, I consider that the fact that Stirling showed that De Moivre's arithmetical constant was ${\sqrt {2\pi }}$ does not entitle him to claim the theorem, [...]
Robbins, Herbert (1955), "A Remark on Stirling's Formula", The American Mathematical Monthly, 62 (1): 26–29, doi:10.2307/2308012, JSTOR 2308012

nist.gov (Global: 355^th place; English: 454^th place)

dlmf.nist.gov

Olver, F. W. J.; Olde Daalhuis, A. B.; Lozier, D. W.; Schneider, B. I.; Boisvert, R. F.; Clark, C. W.; Miller, B. R. & Saunders, B. V., "5.11 Gamma function properties: Asymptotic Expansions", NIST Digital Library of Mathematical Functions, Release 1.0.13 of 2016-09-16

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

Toth, V. T. Programmable Calculators: Calculators and the Gamma Function (2006) Archived 2005-12-31 at the Wayback Machine.

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

api.semanticscholar.org

Dutka, Jacques (1991), "The early history of the factorial function", Archive for History of Exact Sciences, 43 (3): 225–249, doi:10.1007/BF00389433, S2CID 122237769
Flajolet, Philippe; Sedgewick, Robert (2009), Analytic Combinatorics, Cambridge, UK: Cambridge University Press, p. 555, doi:10.1017/CBO9780511801655, ISBN 978-0-521-89806-5, MR 2483235, S2CID 27509971
Nemes, Gergő (2010), "New asymptotic expansion for the Gamma function", Archiv der Mathematik, 95 (2): 161–169, doi:10.1007/s00013-010-0146-9, S2CID 121820640
Mortici, Cristinel (2011), "Ramanujan's estimate for the gamma function via monotonicity arguments", Ramanujan J., 25 (2): 149–154, doi:10.1007/s11139-010-9265-y, S2CID 119530041
Mortici, Cristinel (2011), "On Ramanujan's large argument formula for the gamma function", Ramanujan J., 26 (2): 185–192, doi:10.1007/s11139-010-9281-y, S2CID 120371952.

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

Bayes, Thomas (24 November 1763), "A letter from the late Reverend Mr. Thomas Bayes, F. R. S. to John Canton, M. A. and F. R. S." (PDF), Philosophical Transactions, 53: 269, Bibcode:1763RSPT...53..269B, archived (PDF) from the original on 2012-01-28, retrieved 2012-03-01
Toth, V. T. Programmable Calculators: Calculators and the Gamma Function (2006) Archived 2005-12-31 at the Wayback Machine.

york.ac.uk (Global: 7,670^th place; English: 5,196^th place)

Bayes, Thomas (24 November 1763), "A letter from the late Reverend Mr. Thomas Bayes, F. R. S. to John Canton, M. A. and F. R. S." (PDF), Philosophical Transactions, 53: 269, Bibcode:1763RSPT...53..269B, archived (PDF) from the original on 2012-01-28, retrieved 2012-03-01

Stirling's approximation (English Wikipedia)

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

mathscinet.ams.org

archive.org (Global: 6th place; English: 6th place)

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

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