Gamma function (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Gamma function" in English language version.

refsWebsite

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14doi.org

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5web.archive.org

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5semanticscholar.org

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3books.google.com

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3harvard.edu

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2luschny.de

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2arxiv.org

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2maa.org

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1archive.org

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1nist.gov

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1ams.org

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1jussieu.fr

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1stackexchange.com

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1uni-graz.at

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1ntu.edu.tw

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1worldcat.org

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1researchgate.net

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1ccas.ru

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1dartmouth.edu

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1yearis.com

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1github.com

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aip.org

scitation.aip.org

Berry, M. (April 2001). "Why are special functions special?". Physics Today.

ams.org

mathscinet.ams.org

Askey, R. A.; Roy, R. (2010), "Series Expansions", in Olver, Frank W. J.; Lozier, Daniel M.; Boisvert, Ronald F.; Clark, Charles W. (eds.), NIST Handbook of Mathematical Functions, Cambridge University Press, ISBN 978-0-521-19225-5, MR 2723248.

archive.org

ia800108.us.archive.org

Davis, Philip. "Leonhard Euler's Integral: A Historical Profile of the Gamma Function" (PDF). maa.org.

arxiv.org

Blagouchine, Iaroslav V. (2015). "A theorem for the closed-form evaluation of the first generalized Stieltjes constant at rational arguments and some related summations". Journal of Number Theory. 148: 537–592. arXiv:1401.3724. doi:10.1016/j.jnt.2014.08.009.
Borwein, Jonathan M.; Corless, Robert M. (2017). "Gamma and Factorial in the Monthly". American Mathematical Monthly. 125 (5). Mathematical Association of America: 400–24. arXiv:1703.05349. Bibcode:2017arXiv170305349B. doi:10.1080/00029890.2018.1420983. S2CID 119324101.

att.net

home.att.net

Michon, G. P. "Trigonometry and Basic Functions Archived 9 January 2010 at the Wayback Machine". Numericana. Retrieved 5 May 2007.

books.google.com

Beals, Richard; Wong, Roderick (2010). Special Functions: A Graduate Text. Cambridge University Press. p. 28. ISBN 978-1-139-49043-6. Extract of page 28
Ross, Clay C. (2013). Differential Equations: An Introduction with Mathematica (illustrated ed.). Springer Science & Business Media. p. 293. ISBN 978-1-4757-3949-7. Expression G.2 on page 293
Ilker Inam; Engin Büyükaşşk (2019). Notes from the International Autumn School on Computational Number Theory. Springer. p. 205. ISBN 978-3-030-12558-5. Extract of page 205

ccas.ru

E.A. Karatsuba "Fast Algorithms and the FEE Method".

dartmouth.edu

math.dartmouth.edu

Euler's paper was published in Commentarii academiae scientiarum Petropolitanae 5, 1738, 36–57. See E19 -- De progressionibus transcendentibus seu quarum termini generales algebraice dari nequeunt, from The Euler Archive, which includes a scanned copy of the original article.

doi.org

Davis, P. J. (1959). "Leonhard Euler's Integral: A Historical Profile of the Gamma Function". American Mathematical Monthly. 66 (10): 849–869. doi:10.2307/2309786. JSTOR 2309786. Archived from the original on 7 November 2012. Retrieved 3 December 2016.
Kingman, J. F. C. (1961). "A Convexity Property of Positive Matrices". The Quarterly Journal of Mathematics. 12 (1): 283–284. Bibcode:1961QJMat..12..283K. doi:10.1093/qmath/12.1.283.
Waldschmidt, M. (2006). "Transcendence of Periods: The State of the Art" (PDF). Pure Appl. Math. Quart. 2 (2): 435–463. doi:10.4310/pamq.2006.v2.n2.a3. Archived (PDF) from the original on 6 May 2006.
Blagouchine, Iaroslav V. (2014). "Rediscovery of Malmsten's integrals, their evaluation by contour integration methods and some related results". Ramanujan J. 35 (1): 21–110. doi:10.1007/s11139-013-9528-5. S2CID 120943474.
Blagouchine, Iaroslav V. (2016). "Erratum and Addendum to "Rediscovery of Malmsten's integrals, their evaluation by contour integration methods and some related results"". Ramanujan J. 42 (3): 777–781. doi:10.1007/s11139-015-9763-z. S2CID 125198685.
Blagouchine, Iaroslav V. (2015). "A theorem for the closed-form evaluation of the first generalized Stieltjes constant at rational arguments and some related summations". Journal of Number Theory. 148: 537–592. arXiv:1401.3724. doi:10.1016/j.jnt.2014.08.009.
Adamchik, Victor S. (1998). "Polygamma functions of negative order". J. Comput. Appl. Math. 100 (2): 191–199. doi:10.1016/S0377-0427(98)00192-7.
Espinosa, Olivier; Moll, Victor H. (2002). "On Some Integrals Involving the Hurwitz Zeta Function: Part 1". The Ramanujan Journal. 6 (2): 159–188. doi:10.1023/A:1015706300169. S2CID 128246166.
Bailey, David H.; Borwein, David; Borwein, Jonathan M. (2015). "On Eulerian log-gamma integrals and Tornheim-Witten zeta functions". The Ramanujan Journal. 36 (1–2): 43–68. doi:10.1007/s11139-012-9427-1. S2CID 7335291.
Amdeberhan, T.; Coffey, Mark W.; Espinosa, Olivier; Koutschan, Christoph; Manna, Dante V.; Moll, Victor H. (2011). "Integrals of powers of loggamma". Proc. Amer. Math. Soc. 139 (2): 535–545. doi:10.1090/S0002-9939-2010-10589-0.
Borwein, J. M.; Zucker, I. J. (1992). "Fast evaluation of the gamma function for small rational fractions using complete elliptic integrals of the first kind". IMA Journal of Numerical Analysis. 12 (4): 519–526. doi:10.1093/IMANUM/12.4.519.
Werner, Helmut; Collinge, Robert (1961). "Chebyshev approximations to the Gamma Function". Math. Comput. 15 (74): 195–197. doi:10.1090/S0025-5718-61-99220-1. JSTOR 2004230.
Lanczos, C. (1964). "A precision approximation of the gamma function". Journal of the Society for Industrial and Applied Mathematics, Series B: Numerical Analysis. 1 (1): 86. Bibcode:1964SJNA....1...86L. doi:10.1137/0701008.
Borwein, Jonathan M.; Corless, Robert M. (2017). "Gamma and Factorial in the Monthly". American Mathematical Monthly. 125 (5). Mathematical Association of America: 400–24. arXiv:1703.05349. Bibcode:2017arXiv170305349B. doi:10.1080/00029890.2018.1420983. S2CID 119324101.

github.com

"microsoft/calculator". GitHub. Retrieved 25 December 2020.

gnome.org

gitlab.gnome.org

"gnome-calculator". GNOME.org. Retrieved 3 March 2023.

harvard.edu

ui.adsabs.harvard.edu

Kingman, J. F. C. (1961). "A Convexity Property of Positive Matrices". The Quarterly Journal of Mathematics. 12 (1): 283–284. Bibcode:1961QJMat..12..283K. doi:10.1093/qmath/12.1.283.
Lanczos, C. (1964). "A precision approximation of the gamma function". Journal of the Society for Industrial and Applied Mathematics, Series B: Numerical Analysis. 1 (1): 86. Bibcode:1964SJNA....1...86L. doi:10.1137/0701008.
Borwein, Jonathan M.; Corless, Robert M. (2017). "Gamma and Factorial in the Monthly". American Mathematical Monthly. 125 (5). Mathematical Association of America: 400–24. arXiv:1703.05349. Bibcode:2017arXiv170305349B. doi:10.1080/00029890.2018.1420983. S2CID 119324101.

infn.it

roma1.infn.it

Bonvini, Marco (9 October 2010). "The Gamma function" (PDF). Roma1.infn.it.

jstor.org

Davis, P. J. (1959). "Leonhard Euler's Integral: A Historical Profile of the Gamma Function". American Mathematical Monthly. 66 (10): 849–869. doi:10.2307/2309786. JSTOR 2309786. Archived from the original on 7 November 2012. Retrieved 3 December 2016.
Werner, Helmut; Collinge, Robert (1961). "Chebyshev approximations to the Gamma Function". Math. Comput. 15 (74): 195–197. doi:10.1090/S0025-5718-61-99220-1. JSTOR 2004230.

jussieu.fr

math.jussieu.fr

Waldschmidt, M. (2006). "Transcendence of Periods: The State of the Art" (PDF). Pure Appl. Math. Quart. 2 (2): 435–463. doi:10.4310/pamq.2006.v2.n2.a3. Archived (PDF) from the original on 6 May 2006.

luschny.de

maa.org

mathdl.maa.org

Davis, P. J. (1959). "Leonhard Euler's Integral: A Historical Profile of the Gamma Function". American Mathematical Monthly. 66 (10): 849–869. doi:10.2307/2309786. JSTOR 2309786. Archived from the original on 7 November 2012. Retrieved 3 December 2016.

maa.org

"Leonhard Euler's Integral: An Historical Profile of the Gamma Function" (PDF). Archived (PDF) from the original on 12 September 2014. Retrieved 11 April 2022.

nist.gov

dlmf.nist.gov

Askey, R. A.; Roy, R. (2010), "Series Expansions", in Olver, Frank W. J.; Lozier, Daniel M.; Boisvert, Ronald F.; Clark, Charles W. (eds.), NIST Handbook of Mathematical Functions, Cambridge University Press, ISBN 978-0-521-19225-5, MR 2723248.

ntu.edu.tw

csie.ntu.edu.tw

Pascal Sebah, Xavier Gourdon. "Introduction to the Gamma Function" (PDF). Numbers Computation. Archived from the original (PDF) on 30 January 2023. Retrieved 30 January 2023.

oeis.org

Sloane, N. J. A. (ed.). "Sequence A030169 (Decimal expansion of real number x such that y = Gamma(x) is a minimum)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
Sloane, N. J. A. (ed.). "Sequence A030171 (Decimal expansion of real number y such that y = Gamma(x) is a minimum)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
Sloane, N. J. A. (ed.). "Sequence A178840 (Decimal expansion of the factorial of Golden Ratio)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
Sloane, N. J. A. (ed.). "Sequence A175472 (Decimal expansion of the absolute value of the abscissa of the local maximum of the Gamma function in the interval [ -1,0])". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
Sloane, N. J. A. (ed.). "Sequence A175473 (Decimal expansion of the absolute value of the abscissa of the local minimum of the Gamma function in the interval [ -2,-1])". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
Sloane, N. J. A. (ed.). "Sequence A175474 (Decimal expansion of the absolute value of the abscissa of the local maximum of the Gamma function in the interval [ -3,-2])". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
Sloane, N. J. A. (ed.). "Sequence A256681 (Decimal expansion of the [negated] abscissa of the Gamma function local minimum in the interval [-4,-3])". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
Sloane, N. J. A. (ed.). "Sequence A256682 (Decimal expansion of the [negated] abscissa of the Gamma function local maximum in the interval [-5,-4])". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
Sloane, N. J. A. (ed.). "Sequence A245886 (Decimal expansion of Gamma(-3/2), where Gamma is Euler's gamma function)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
Sloane, N. J. A. (ed.). "Sequence A019707 (Decimal expansion of sqrt(Pi)/5)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
Sloane, N. J. A. (ed.). "Sequence A002161 (Decimal expansion of square root of Pi)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
Sloane, N. J. A. (ed.). "Sequence A019704 (Decimal expansion of sqrt(Pi)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
Sloane, N. J. A. (ed.). "Sequence A245884 (Decimal expansion of Gamma(5/2), where Gamma is Euler's gamma function)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
Sloane, N. J. A. (ed.). "Sequence A245885 (Decimal expansion of Gamma(7/2), where Gamma is Euler's gamma function)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

researchgate.net

Blagouchine, Iaroslav V. (2014). "Rediscovery of Malmsten's integrals, their evaluation by contour integration methods and some related results". Ramanujan J. 35 (1): 21–110. doi:10.1007/s11139-013-9528-5. S2CID 120943474.

semanticscholar.org

api.semanticscholar.org

Blagouchine, Iaroslav V. (2014). "Rediscovery of Malmsten's integrals, their evaluation by contour integration methods and some related results". Ramanujan J. 35 (1): 21–110. doi:10.1007/s11139-013-9528-5. S2CID 120943474.
Blagouchine, Iaroslav V. (2016). "Erratum and Addendum to "Rediscovery of Malmsten's integrals, their evaluation by contour integration methods and some related results"". Ramanujan J. 42 (3): 777–781. doi:10.1007/s11139-015-9763-z. S2CID 125198685.
Espinosa, Olivier; Moll, Victor H. (2002). "On Some Integrals Involving the Hurwitz Zeta Function: Part 1". The Ramanujan Journal. 6 (2): 159–188. doi:10.1023/A:1015706300169. S2CID 128246166.
Bailey, David H.; Borwein, David; Borwein, Jonathan M. (2015). "On Eulerian log-gamma integrals and Tornheim-Witten zeta functions". The Ramanujan Journal. 36 (1–2): 43–68. doi:10.1007/s11139-012-9427-1. S2CID 7335291.
Borwein, Jonathan M.; Corless, Robert M. (2017). "Gamma and Factorial in the Monthly". American Mathematical Monthly. 125 (5). Mathematical Association of America: 400–24. arXiv:1703.05349. Bibcode:2017arXiv170305349B. doi:10.1080/00029890.2018.1420983. S2CID 119324101.

stackexchange.com

math.stackexchange.com

"How to obtain the Laurent expansion of gamma function around $z=0$?". Mathematics Stack Exchange. Retrieved 17 August 2022.

uni-graz.at

imsc.uni-graz.at

Detlef, Gronau. "Why is the gamma function so as it is?" (PDF). Imsc.uni-graz.at.

web.archive.org

Davis, P. J. (1959). "Leonhard Euler's Integral: A Historical Profile of the Gamma Function". American Mathematical Monthly. 66 (10): 849–869. doi:10.2307/2309786. JSTOR 2309786. Archived from the original on 7 November 2012. Retrieved 3 December 2016.
Waldschmidt, M. (2006). "Transcendence of Periods: The State of the Art" (PDF). Pure Appl. Math. Quart. 2 (2): 435–463. doi:10.4310/pamq.2006.v2.n2.a3. Archived (PDF) from the original on 6 May 2006.
Pascal Sebah, Xavier Gourdon. "Introduction to the Gamma Function" (PDF). Numbers Computation. Archived from the original (PDF) on 30 January 2023. Retrieved 30 January 2023.
"Leonhard Euler's Integral: An Historical Profile of the Gamma Function" (PDF). Archived (PDF) from the original on 12 September 2014. Retrieved 11 April 2022.
Michon, G. P. "Trigonometry and Basic Functions Archived 9 January 2010 at the Wayback Machine". Numericana. Retrieved 5 May 2007.

wolfram.com

mathworld.wolfram.com

Weisstein, Eric W. "Bohr–Mollerup Theorem". MathWorld.
Weisstein, Eric W. "Gamma Function". MathWorld.
"Log Gamma Function". Wolfram MathWorld. Retrieved 3 January 2019.

functions.wolfram.com

worldcat.org

search.worldcat.org

Bateman, Harry; Erdélyi, Arthur (1955). Higher Transcendental Functions. McGraw-Hill. OCLC 627135.

yearis.com

"What's the history of Gamma_function?". yearis.com. Retrieved 5 November 2022.