Editing Gamma function (section)

=== Reference tables and software ===

Although the gamma function can be calculated virtually as easily as any mathematically simpler function with a modern computer—even with a programmable pocket calculator—this was of course not always the case. Until the mid-20th century, mathematicians relied on hand-made tables; in the case of the gamma function, notably a table computed by Gauss in 1813 and one computed by Legendre in 1825.<ref>{{Cite web |title=What's the history of Gamma_function? |url=https://yearis.com/gamma_function/ |access-date=2022-11-05 |website=yearis.com}}</ref>

[[File:Jahnke gamma function.png|thumb|300px|A hand-drawn graph of the absolute value of the complex gamma function, from ''Tables of Higher Functions'' by [[Eugen Jahnke|Jahnke]] and {{ill|Fritz Emde|de|lt=Emde}}.]]

Tables of complex values of the gamma function, as well as hand-drawn graphs, were given in ''[[Tables of Functions With Formulas and Curves]]'' by [[Eugen Jahnke|Jahnke]] and {{ill|Fritz Emde|de|lt=Emde}}, first published in Germany in 1909. According to [[Michael Berry (physicist)|Michael Berry]], "the publication in J&E of a three-dimensional graph showing the poles of the gamma function in the complex plane acquired an almost iconic status."<ref>{{cite news|last=Berry |first=M. |url=http://scitation.aip.org/journals/doc/PHTOAD-ft/vol_54/iss_4/11_1.shtml?bypassSSO=1 |title=Why are special functions special? |newspaper=Physics Today |date=April 2001}}</ref>

There was in fact little practical need for anything but real values of the gamma function until the 1930s, when applications for the complex gamma function were discovered in theoretical physics. As electronic computers became available for the production of tables in the 1950s, several extensive tables for the complex gamma function were published to meet the demand, including a table accurate to 12 decimal places from the U.S. [[National Bureau of Standards]].<ref name=Davis />
[[File:Famous complex plot by Janhke and Emde (Tables of Functions with Formulas and Curves, 4th ed., Dover, 1945) gamma function from -4.5-2.5i to 4.5+2.5i.svg|alt=Reproduction of a famous complex plot by Janhke and Emde (Tables of Functions with Formulas and Curves, 4th ed., Dover, 1945) of the gamma function from −4.5 − 2.5i to 4.5 + 2.5i|thumb|Reproduction of a famous complex plot by Janhke and Emde (Tables of Functions with Formulas and Curves, 4th ed., Dover, 1945) of the gamma function from −4.5 − 2.5i to 4.5 + 2.5i]]
Double-precision floating-point implementations of the gamma function and its logarithm are now available in most scientific computing software and special functions libraries, for example [[TK Solver]], [[Matlab]], [[GNU Octave]], and the [[GNU Scientific Library]]. The gamma function was also added to the [[C (programming language)|C]] standard library ([[math.h]]). Arbitrary-precision implementations are available in most [[computer algebra system]]s, such as [[Mathematica]] and [[Maple (software)|Maple]]. [[PARI/GP]], [[MPFR]] and [[MPFUN]] contain free arbitrary-precision implementations. In some [[software calculator]]s, e.g. [[Windows Calculator]] and [[GNOME]] Calculator, the factorial function returns Γ(''x'' + 1) when the input ''x'' is a non-integer value.<ref>{{Cite web|title=microsoft/calculator|url=https://github.com/microsoft/calculator|access-date=2020-12-25|website=GitHub|language=en}}</ref><ref>{{Cite web|title=gnome-calculator|url=https://gitlab.gnome.org/GNOME/gnome-calculator|access-date=2023-03-03|website=GNOME.org|language=en}}</ref>

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