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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.
It is unknown whether these constants are transcendental in general, but Γ( 1 / 3 ) and Γ( 1 / 4 ) were shown to be transcendental by G. V. Chudnovsky. Γ( 1 / 4 ) / 4 √ π has also long been known to be transcendental, and Yuri Nesterenko proved in 1996 that Γ( 1 / 4 ), π, and e π are algebraically independent.
In mathematics, the p-adic gamma function Γ p is a function of a p-adic variable analogous to the gamma function. It was first explicitly defined by Morita (1975), though Boyarsky (1980) pointed out that Dwork (1964) implicitly used the same function. Diamond (1977) defined a p-adic analog G p of log Γ.
The Nakagami distribution or the Nakagami-m distribution is a probability distribution related to the gamma distribution. The family of Nakagami distributions has two parameters: a shape parameter m ≥ 1 / 2 {\displaystyle m\geq 1/2} and a scale parameter Ω > 0 {\displaystyle \Omega >0} .
The reciprocal is sometimes used as a starting point for numerical computation of the gamma function, and a few software libraries provide it separately from the regular gamma function. Karl Weierstrass called the reciprocal gamma function the "factorielle" and used it in his development of the Weierstrass factorization theorem .
On some operating systems running the X Window System, one can set the gamma correction factor (applied to the existing gamma value) by issuing the command xgamma -gamma 0.9 for setting gamma correction factor to 0.9, and xgamma for querying current value of that factor (the default is 1.0). In macOS systems, the gamma and other related screen ...
The perceptual quantizer (PQ), published by SMPTE as SMPTE ST 2084, [1] is a transfer function that allows for HDR display by replacing the gamma curve used in SDR ...
for which a ≡ d ≡ ±1 (mod N) and b ≡ c ≡ 0 (mod N). It is easy to show that the trace of a matrix representing an element of Γ(N) cannot be −1, 0, or 1, so these subgroups are torsion-free groups. (There are other torsion-free subgroups.) The principal congruence subgroup of level 2, Γ(2), is also called the modular group Λ.
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