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1. Gamma function - Wikipedia
wikipedia.org
Link: https://en.wikipedia.org/wiki/Gamma_function
Description: WebIn mathematics, the gamma function (represented by Γ, the capital letter gamma from the Greek alphabet) is one commonly used extension of the factorial function to complex numbers. The gamma function is defined for all complex numbers except the …
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2. Gamma Function -- from Wolfram MathWorld
wolfram.com
Link: https://mathworld.wolfram.com/GammaFunction.html
Description: Web3 days ago · The (complete) gamma function Gamma(n) is defined to be an extension of the factorial to complex and real number arguments. It is related to the factorial by Gamma(n)=(n-1)!, (1) a slightly unfortunate notation due to Legendre which is now universally used instead of Gauss's simpler Pi(n)=n!
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3. 14.2: Definition and properties of the Gamma function
libretexts.org
Link: https://math.libretexts.org/Bookshelves/Analysis/Complex_Variables_with_Applications_(Orloff)/14%3A_Analytic_Continuation_and_the_Gamma_Function/14.02%3A_Definition_and_properties_of_the_Gamma_function
Description: WebMassachusetts Institute of Technology via MIT OpenCourseWare. Definition: Gamma Function. The Gamma function is defined by the integral formula. Γ(z) = ∫∞ 0 tz−1e−t dt Γ ( z) = ∫ 0 ∞ t z − 1 e − t d t. The integral converges absolutely for Re(z) > 0 Re ( z) > 0.
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4. Gamma Function - Math is Fun
mathsisfun.com
Link: https://www.mathsisfun.com/numbers/gamma-function.html
Description: WebGamma Function. The Gamma Function serves as a super powerful version of the factorial function. Let us first look at the factorial function: The factorial function (symbol: !) says to multiply all whole numbers from our chosen number down to 1. Examples: 4! = 4 × 3 × 2 × 1 = 24. 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040. 1! = 1.
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5. Gamma Function | Brilliant Math & Science Wiki
brilliant.org
Link: https://brilliant.org/wiki/gamma-function/
Description: Web17 others. contributed. The gamma function, denoted by \Gamma (s) Γ(s), is defined by the formula. \Gamma (s)=\int_0^ {\infty} t^ {s-1} e^ {-t}\, dt, Γ(s) = ∫ 0∞ ts−1e−tdt, which is defined for all complex numbers except the nonpositive integers. It is frequently used in identities and proofs in analytic contexts.
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6. Gamma function: Introduction to the Gamma Function - Wolfram
wolfram.com
Link: https://functions.wolfram.com/GammaBetaErf/Gamma/introductions/Gamma/ShowAll.html
Description: WebThe gamma function is used in the mathematical and applied sciences almost as often as the well-known factorial symbol . It was introduced by the famous mathematician L. Euler (1729) as a natural extension of the factorial operation from positive integers to real and even complex values of the argument .
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7. Gamma function | Properties, Examples, & Equation | Britannica
britannica.com
Link: https://www.britannica.com/science/gamma-function
Description: WebFeb 25, 2024 · gamma function, generalization of the factorial function to nonintegral values, introduced by the Swiss mathematician Leonhard Euler in the 18th century. For a positive whole number n, the factorial (written as n!) is defined by n! = 1 × 2 × 3 ×⋯× (n − 1) × n. For example, 5! = 1 × 2 × 3 × 4 × 5 = 120.
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8. Gamma function | Definition, properties, proofs - Statlect
statlect.com
Link: https://www.statlect.com/mathematical-tools/gamma-function
Description: WebGamma function. by Marco Taboga, PhD. The Gamma function is a generalization of the factorial function to non-integer numbers. It is often used in probability and statistics, as it shows up in the normalizing constants of important probability distributions such as the Chi-square and the Gamma.
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9. Notes on Gamma and Zeta - University of California, Berkeley
berkeley.edu
Link: https://math.berkeley.edu/~mhaiman/math185-summer14/gamma-notes.pdf
Description: WebThe gamma function ( z), as de ned by (1), has an analytic continuation (necessarily unique) to the domain C f 0; 1; 2;:::g, and satis es (2) for all zin this domain. From here on, ( z) will stand for the gamma function analytically continued …
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10. Gamma function: Introduction to the gamma functions - Wolfram
wolfram.com
Link: https://functions.wolfram.com/GammaBetaErf/Gamma/introductions/Gammas/ShowAll.html
Description: WebThe gamma functions are used throughout mathematics, the exact sciences, and engineering. In particular, the incomplete gamma function is used in solid state physics and statistics, and the logarithm of the gamma function is used in discrete mathematics, number theory, and other fields of sciences.
