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  2. Gamma function - Wikipedia

    en.wikipedia.org/wiki/Gamma_function

    The gamma function then is defined in the complex plane as the analytic continuation of this integral function: it is a meromorphic function which is holomorphic except at zero and the negative integers, where it has simple poles. The gamma function has no zeros, so the reciprocal gamma function ⁠ 1 / Γ(z) ⁠ is an entire function.

  3. Particular values of the gamma function - Wikipedia

    en.wikipedia.org/wiki/Particular_values_of_the...

    The gamma function is an important special function in mathematics.Its particular values can be expressed in closed form for integer and half-integer arguments, but no simple expressions are known for the values at rational points in general.

  4. Gamma distribution - Wikipedia

    en.wikipedia.org/wiki/Gamma_distribution

    The cumulative distribution function is the regularized gamma function: (; ... It is sometimes referred to as the log-gamma distribution. [20] Formulas for its mean ...

  5. Incomplete gamma function - Wikipedia

    en.wikipedia.org/wiki/Incomplete_gamma_function

    Repeated application of the recurrence relation for the lower incomplete gamma function leads to the power series expansion: [2] (,) = = (+) (+) = = (+ +). Given the rapid growth in absolute value of Γ(z + k) when k → ∞, and the fact that the reciprocal of Γ(z) is an entire function, the coefficients in the rightmost sum are well-defined, and locally the sum converges uniformly for all ...

  6. Lanczos approximation - Wikipedia

    en.wikipedia.org/wiki/Lanczos_approximation

    Thus computing the gamma function becomes a matter of evaluating only a small number of elementary functions and multiplying by stored constants. The Lanczos approximation was popularized by Numerical Recipes , according to which computing the gamma function becomes "not much more difficult than other built-in functions that we take for granted ...

  7. Stirling's approximation - Wikipedia

    en.wikipedia.org/wiki/Stirling's_approximation

    However, the gamma function, unlike the factorial, is more broadly defined for all complex numbers other than non-positive integers; nevertheless, Stirling's formula may still be applied.

  8. Barnes G-function - Wikipedia

    en.wikipedia.org/wiki/Barnes_G-function

    In mathematics, the Barnes G-function G(z) is a function that is an extension of superfactorials to the complex numbers. It is related to the gamma function, the K-function and the Glaisher–Kinkelin constant, and was named after mathematician Ernest William Barnes. [1] It can be written in terms of the double gamma function.

  9. q-gamma function - Wikipedia

    en.wikipedia.org/wiki/Q-gamma_function

    In q-analog theory, the -gamma function, or basic gamma function, is a generalization of the ordinary gamma function closely related to the double gamma function. It was introduced by Jackson (1905) .