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Gamma (/ ˈɡæmə /; [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].
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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.
Gamma ray, electromagnetic radiation of the shortest wavelength and highest energy. Gamma rays are produced in the disintegration of radioactive atomic nuclei and in the decay of certain subatomic particles. It includes some overlap with X-rays in the electromagnetic spectrum.
The 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 .
