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Gamma function

In mathematics, the gamma function (represented by ⁠ Γ {\displaystyle \Gamma } ⁠, capital Greek letter gamma) is the most common extension of the factorial function to complex numbers. First studied by Daniel Bernoulli, the gamma function Γ ( z ) {\displaystyle \Gamma (z)} is defined for all complex numbers z {\displaystyle z} except non-positive integers…

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Fields of application
Calculus, mathematical analysis, statistics, physics
General definition
Γ ( z ) = ∫ 0 ∞ t z − 1 e − t d t {\displaystyle \Gamma (z)=\int _{0}^{\infty }t^{z-1}e^{-t}\,dt}

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Log-gamma function

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Gamma function

Nodes183
Edges182
Triples225
Avg. degree1.99
Density0.010929
Components1

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Gamma function

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related to External links · 22
Gamma function → Archived, C99, EMS Press, Encyclopedia, Exampleproblems, Gamma, HTML, In PostScript, Introduction, Mathematical Functions, Mathematics, MathPages, NIST Digital Library, October, Postgres, Sebah, Spheres, Volume, Wayback Machine, Wolfram
related to 18th century: Euler and Stirling · 18
Gamma function → Bernoulli, By, Christian Goldbach, Daniel Bernoulli, De, Euler, Goldbach, He, In, January, Leonhard Euler, November, October, On, Petersburg Academy, Re, St, The
related to Practical implementations · 13
Gamma function → For, Gamma, Greater, If, Internet, Lanczos, Online Wiley Library, Since, Stirling's, Such, Therefore, Unlike, When
related to 19th–20th centuries: characterizing the gamma function · 12
Gamma function → Although, Charles Hermite, Euler's, However, Hölder's, Instead, It, Most, One, Otto Hölder, Stirling, This
related to Reference tables and software · 12
Gamma function → According, Although, Curves, Emde, Functions With Formulas, Gauss, Germany, Jahnke, Legendre, Michael Berry, Tables, Until
related to Relation to other functions · 12
Gamma function → Euler's, For, Gamma, Gaussian, Hurwitz, In, It, Lerch, Re, Riemann, The, There
related to 19th century: Gauss, Weierstrass, and Legendre · 10
Gamma function → Although Euler, Carl Friedrich Gauss, Euler, Euler's, Gamma, Gauss, Inspired, Karl Weierstrass, Mascheroni, Weierstrass
related to Integral representations · 10
Gamma function → Binet's, Euler, Euler's, For, Gamma, Gaussian, Laplace, That, The, There
is a · 9
Gamma function → continuous analogue of a Gauss sum, continuous analogue of a Gauss sum.19th, entire function and has been studied as a specific topic.The gamma function also shows up in an important relation with the Riemann zeta function, integral of the additive character e, most popular and useful, strictly logarithmically convex function, study of the Riemann zeta function, unique function that simultaneously satisfies, unique solution to the factorial recurrence relation that is positive and logarithmically convex for positive
related to Residues · 8
Gamma function → Euler's, For, Gamma, One, Re, Res, The, Thus

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gamma displaystyle function frac infty left right pi formula integral log complex int positive real numbers functions -1 factorial also

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SubjectPredicateObjectConfidenceSrc
Gamma functionFields of applicationCalculus, mathematical analysis, statistics, physics1.00infobox
Gamma functionGeneral definitionΓ ( z ) = ∫ 0 ∞ t z − 1 e − t d t {\displaystyle \Gamma (z)=\int _{0}^{\infty }t^{z-1}e^{-t}\,dt}1.00infobox
Gamma functionis amost popular and useful0.90text
Gamma functionis astrictly logarithmically convex function0.90text
Gamma functionis aentire function and has been studied as a specific topic.The gamma function also shows up in an important relation with the Riemann zeta function0.90text
Gamma functionis aunique function that simultaneously satisfies0.90text
Gamma functionis astudy of the Riemann zeta function0.90text
Gamma functionis aintegral of the additive character e0.90text
Gamma functionis acontinuous analogue of a Gauss sum.19th0.90text
Gamma functionis aunique solution to the factorial recurrence relation that is positive and logarithmically convex for positive0.90text
Gamma functionis acontinuous analogue of a Gauss sum0.90text
probability theoryinstance ofand by extension in areas0.80text

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