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A gamma ray, also known as gamma radiation (symbol γ), is a penetrating form of electromagnetic radiation arising from high energy interactions like the radioactive decay of atomic nuclei or astronomical events like solar flares. It consists of the shortest wavelength electromagnetic waves, typically shorter than those of X-rays.
Gamma (/ ˈ ɡ æ m ə /; [1] uppercase Γ, lowercase γ; Greek: γάμμα, romanized: gámma) is the third letter of the Greek alphabet. In the system of Greek numerals it has a value of 3. In Ancient Greek , the letter gamma represented a voiced velar stop IPA: [ɡ] .
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.
The defining property for the gamma matrices to generate a Clifford algebra is the anticommutation relation {,} = + = ,where the curly brackets {,} represent the anticommutator, is the Minkowski metric with signature (+ − − −), and is the 4 × 4 identity matrix.
In Bayesian inference, the gamma distribution is the conjugate prior to many likelihood distributions: the Poisson, exponential, normal (with known mean), Pareto, gamma with known shape σ, inverse gamma with known shape parameter, and Gompertz with known scale parameter.
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.
A gamma wave or gamma rhythm is a pattern of neural oscillation in humans with a frequency between 30 and 100 Hz, the 40 Hz point being of particular interest. [1] Gamma waves with frequencies between 30 and 70 hertz may be classified as low gamma , and those between 70 and 150 hertz as high gamma .
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 ...