where Γ ( z ) is the gamma function, a generalization of the factorial function to non-integer values.

Here the left-hand side is equal to, namely the first-order polygamma function defined through ; the gamma function is equal to if is a positive integer.

* In mathematics, the gamma function ( usually written as-function ) is an extension of the factorial to complex numbers

The gamma function along part of the real axis

In mathematics, the gamma function ( represented by the capital Greek letter Γ ) is an extension of the factorial function, with its argument shifted down by 1, to real and complex numbers.

The gamma function is defined for all complex numbers except the non-positive integers.

This integral function is extended by analytic continuation to all complex numbers except the non-positive integers ( where the function has simple poles ), yielding the meromorphic function we call the gamma function.

The gamma function can be seen as a solution to the following interpolation problem:

Asymptotically as, the magnitude of the gamma function is given by Stirling's formula

Thus, the gamma function must be undefined at those points ; it is a meromorphic function with simple poles at the nonpositive integers.

The following image shows the graph of the gamma function along the real line:

The gamma function is nonzero everywhere along the real line, although it comes arbitrarily close as.

There is in fact no complex number z for which, and hence the reciprocal gamma function is an entire function, with zeros at z = 0, − 1, − 2 ,.... We see that the gamma function has a local minimum at where it attains the value.

In some amino acids, the amine group is attached to the β or γ-carbon, and these are therefore referred to as beta or gamma amino acids.

Even touching an alpha source is usually not harmful, though many alpha sources also are accompanied by beta-emitting radio daughters, and alpha emission is also accompanied by gamma photon emission.

The relative biological effectiveness ( RBE ) of alpha radiation is higher than that of beta or gamma radiation.

The presence of the resulting antimatter is detectable by the two gamma rays produced every time positrons annihilate with nearby matter.

As a metal, beryllium is transparent to most wavelengths of X-rays and gamma rays, making it useful for the output windows of X-ray tubes and other such apparatus.

If it were, there would be X-rays and gamma rays produced as a result of annihilation, but this is not observed.

One idea that has drawn attention for several decades is that consciousness is associated with high-frequency ( gamma band ) oscillations in brain activity.

Several radioactive substances are considered carcinogens, but their carcinogenic activity is attributed to the radiation, for example gamma rays and alpha particles, which they emit.

By contrast, for higher frequency radiations at ultraviolet frequencies and above ( i. e., X-rays and gamma rays ) the damage to chemical materials and living cells by EMR is far larger than that done by simple heating, due to the ability of single photons in such high frequency EMR to damage individual molecules chemically.

In general, EM radiation ( the designation ' radiation ' excludes static electric and magnetic and near fields ) is classified by wavelength into radio, microwave, infrared, the visible spectrum we perceive as visible light, ultraviolet, X-rays, and gamma rays.

This is most obvious in the " far " ( or " extreme ") ultraviolet, and also X-ray and gamma radiation, are referred to as ionizing radiation due to the ability of photons of this radiation to produce ions and free radicals in materials ( including living tissue ).

Noninvasive surgery using the gamma knife or other devices used in radiosurgery is currently being investigated as an alternative to traditional open surgery in patients who would otherwise qualify for anterior temporal lobectomy.

Irradiation of food is the exposure of food to ionizing radiation ; either high-energy electrons or X-rays from accelerators, or by gamma rays ( emitted from radioactive sources as Cobalt-60 or Caesium-137 ).

The first carbon atom after the carbon that attaches to the functional group is called the alpha carbon ; the second, beta carbon, the third, gamma carbon, etc.

Thus, a practical fallout shield is ten halving-thicknesses of packed dirt, reducing gamma rays by approximately 1024 times ( 2 < sup > 10 </ sup >).

* the power by which the luminance of an image is increased in gamma correction

** The shear rate of a fluid is represented by a lower case gamma with a dot above it:

* In probability theory and statistics, the gamma distribution is a two-parameter family of continuous probability distributions.

Briefly, the specification calls for picture encoding using the ISO / IEC 15444-1 " JPEG2000 " (. jp2 ) standard and use of the CIE XYZ color space at 12 bits per component encoded with a 2. 6 gamma applied at projection, and audio using the " Broadcast Wave " (. wav ) format at 24 bits and 48 kHz or 96 kHz sampling, controlled by an XML-format Composition Playlist, into an MXF-compliant file at a maximum data rate of 250 Mbit / s.

In dimension 3, defining the gamma matrices to be the Pauli sigma matrices gives rise to the familiar two component spinors used in non relativistic quantum mechanics.

Likewise using the 4 × 4 Dirac gamma matrices gives rise to the 4 component Dirac spinors used in 3 + 1 dimensional relativistic quantum field theory.

The E1 component is produced when gamma radiation from the nuclear detonation knocks electrons out of the atoms in the upper atmosphere.

The E2 component is generated by scattered gamma rays and inelastic gammas produced by weapon neutrons.

Since the E1 component of nuclear EMP depends on the prompt gamma ray output, which was only 0. 1 % of yield in Starfish Prime but can be 0. 5 % of yield in pure fission weapons of low yield, a 10 kiloton bomb can easily be 5 x 8 % = 40 % as powerful as the 1. 44 megaton Starfish Prime at producing EMP.

The important E1 component is generated by interaction with the electrons in the upper atmosphere that are hit by gamma radiation from the weapon — and the subsequent effects upon those electrons by the Earth's magnetic field.

When materials are exposed to short-wavelength X-rays or to gamma rays, ionization of their component atoms may take place.

Y ' stands for the luma component ( the brightness ) and U and V are the chrominance ( color ) components ; luminance is denoted by Y and luma by Y ' – the prime symbols (') denote gamma compression, with " luminance " meaning perceptual ( color science ) brightness, while " luma " is electronic ( voltage of display ) brightness.

Ultimately, the neutron component of initial radiation becomes negligible in comparison with the gamma component.

This group is related to the octonions by considering the 16 component spinors as two component octonion spinors and the gamma matrices acting on the upper indices as unit octonions.

The main component of the 8π spectrometer are the Hyper-pure Germanium detectors used to observe gamma rays emitted from excited states of daughter nuclei.

In this case, VB would compute optimum estimates of the four parameters of the normal-scaled inverse gamma distribution that describes the joint distribution of the mean and variance of the component.

Any negative can be reproduced on the recorder retaining the original neg's characteristics ( such as color component crosstalk and gamma ) — and thereby retaining the negative's " look " if it were directly printed.

The longer half-lived iodine-125 is also occasionally used when a longer half-life radioiodine is needed for diagnosis, and, in brachytherapy treatment ( isotope confined in small seed-like metal capsules ), where the low-energy gamma radiation without a beta component, makes iodine-125 useful.

Gamma motoneurons ( γ-motoneurons ), also called gamma motor neurons, are the efferent component of the fusimotor system, the system by which the central nervous system controls and modifies muscle spindle sensitivity.