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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. Other fractional arguments can be approximated through efficient infinite products, infinite series ...
In astrophysics, gamma rays are conventionally defined as having photon energies above 100 keV and are the subject of gamma-ray astronomy, while radiation below 100 keV is classified as X-rays and is the subject of X-ray astronomy. Gamma rays are ionizing radiation and are thus hazardous to life.
The incoming gamma ray effectively knocks one or more neutrons, protons, or an alpha particle out of the nucleus. [1] The reactions are called (γ,n), (γ,p), and (γ,α), respectively. Photodisintegration is endothermic (energy absorbing) for atomic nuclei lighter than iron and sometimes exothermic (energy releasing) for atomic nuclei heavier ...
the gamma function, a generalization of the factorial [2] the upper incomplete gamma function; the modular group, the group of fractional linear transformations; the gamma distribution, a continuous probability distribution defined using the gamma function; second-order sensitivity to price in mathematical finance
The various multipole fields have particular values of angular momentum: E radiation carries an angular momentum in units of ; likewise, M radiation carries an angular momentum in units of . The conservation of angular momentum leads to selection rules , i.e., rules defining which multipoles may or may not be emitted in particular transitions.
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.
A fast algorithm for calculation of the Euler gamma function for any algebraic argument (including rational) was constructed by E.A. Karatsuba. [52] [53] [54] For arguments that are integer multiples of 1 / 24 , the gamma function can also be evaluated quickly using arithmetic–geometric mean iterations (see particular values of the ...
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 ...