gamma function - определение. Что такое gamma function
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Что (кто) такое gamma function - определение

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Gamma function         
  • [[Daniel Bernoulli]]'s letter to [[Christian Goldbach]], October 6, 1729
  • The first page of Euler's paper
  • The gamma function interpolates the factorial function to non-integer values.
  • reproduction of a famous complex plot by Janhke and Emde (Tables of Functions with Formulas and Curves, 4th ed., Dover, 1945) of the gamma function from -4.5-2.5i to 4.5+2.5i
  • 3-dimensional plot of the absolute value of the complex gamma function
  • </math> is also displayed.
  • Γ(''z'') + sin(π''z'')}} in green. Notice the intersection at positive integers. Both are valid analytic continuations of the factorials to the non-integers.
  • lt=Emde}}.
  • log Γ(''z'')}}
  • Comparison gamma (blue line) with the factorial (blue dots) and Stirling's approximation (red line)
  • Plot of gamma function in complex plane in 3D with color and legend and 1000 plot points created with Mathematica
  • 6+2''i''}} with colors created in Mathematica
  • Plot of logarithmic gamma function in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D
EXTENSION OF THE FACTORIAL FUNCTION, WITH ITS ARGUMENT SHIFTED DOWN BY 1, TO REAL AND COMPLEX NUMBERS
Gamma-function; Complete gamma function; Gamma Function; Gamma integral; Euler Gamma Function; Γ(x); Γ function; Raabe's formula; Approximations of the gamma function; Weierstrass definition of the gamma function; Complex number factorial
In mathematics, the gamma function (represented by , the capital letter gamma from the Greek alphabet) is one commonly used extension of the factorial function to complex numbers. The gamma function is defined for all complex numbers except the non-positive integers.
https://en.wikipedia.org/wiki/Gamma_function
Multiple gamma function         
  • Plot of the Barnes G aka double gamma function G(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D
GENERALIZATION OF THE EULER GAMMA FUNCTION AND THE BARNES G-FUNCTION
Barnes gamma function; Double gamma function; Triple gamma function; Barnes multiple gamma function; Multiple Gamma function
In mathematics, the multiple gamma function \Gamma_N is a generalization of the Euler gamma function and the Barnes G-function. The double gamma function was studied by .
https://en.wikipedia.org/wiki/Multiple_gamma_function
Q-gamma function         
Q-ANALOG OF THE GAMMA FUNCTION
Q-Gamma function; Basic gamma function; Q gamma function
In q-analog theory, the q-gamma function, or basic gamma function, is a generalization of the ordinary gamma function closely related to the double gamma function. It was introduced by .
https://en.wikipedia.org/wiki/Q-gamma_function
Incomplete gamma function         
  • Plot of the regularized incomplete gamma function Q(2,z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D
TYPES OF SPECIAL MATHEMATICAL FUNCTIONS
Incomplete Gamma function; Regularized gamma function; Regularized Gamma function; Incomplete gamma-function; Incomplete Gamma-function; Upper incomplete gamma function; Lower incomplete gamma function; Derivatives of the incomplete gamma function; Gamma incomplete
In mathematics, the upper and lower incomplete gamma functions are types of special functions which arise as solutions to various mathematical problems such as certain integrals.
https://en.wikipedia.org/wiki/Incomplete_gamma_function
Hadamard's gamma function         
  • Hadamard's gamma function plotted over part of the real axis. Unlike the classical gamma function, it is holomorphic; there are no poles.
EXTENSION OF THE FACTORIAL FUNCTION DIFFERENT FROM THE GAMMA FUNCTION.
Hadamard’s gamma function; Hadamard's Gamma function; Hadamard's Gamma Function
In mathematics, Hadamard's gamma function, named after Jacques Hadamard, is an extension of the factorial function, different from the classical gamma function. This function, with its argument shifted down by 1, interpolates the factorial and extends it to real and complex numbers in a different way than Euler's gamma function.
https://en.wikipedia.org/wiki/Hadamard's_gamma_function
Particular values of the gamma function         
MATHEMATICAL CONSTANTS
Particular values of the Gamma function
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.
https://en.wikipedia.org/wiki/Particular_values_of_the_gamma_function
Gamma ray         
  • Gamma emission spectrum of cobalt-60
  • The total absorption coefficient of aluminium (atomic number 13) for gamma rays, plotted versus gamma energy, and the contributions by the three effects. As is usual, the photoelectric effect is largest at low energies, Compton scattering dominates at intermediate energies, and pair production dominates at high energies.
  • Alpha radiation]] consists of [[helium]] nuclei and is readily stopped by a sheet of paper. [[Beta radiation]], consisting of [[electron]]s or [[positron]]s, is stopped by an aluminium plate, but gamma radiation requires shielding by dense material such as lead or concrete.
  • The red dots show some of the ~500 terrestrial gamma-ray flashes daily detected by the Fermi Gamma-ray Space Telescope through 2010. Credit: NASA/Goddard Space Flight Center.
  • 60}}
  • NASA guide to electromagnetic spectrum showing overlap of frequency between X-rays and gamma rays
  • In practice, gamma ray energies overlap with the range of X-rays, especially in the higher-frequency region referred to as "hard" X-rays. This depiction follows the older convention of distinguishing by wavelength.
  • Image of entire sky in 100 MeV or greater gamma rays as seen by the EGRET instrument aboard the [[CGRO]] spacecraft. Bright spots within the galactic plane are [[pulsar]]s while those above and below the plane are thought to be [[quasar]]s.
  • A [[hypernova]]. Artist's illustration showing the life of a [[massive star]] as [[nuclear fusion]] converts lighter elements into heavier ones. When fusion no longer generates enough pressure to counteract gravity, the star rapidly collapses to form a [[black hole]]. Theoretically, energy may be released during the collapse along the axis of rotation to form a long duration [[gamma-ray burst]].
  • access-date=2011-11-08}}</ref>
  • Fermi's]] Large Area Telescope (LAT).
  • The total absorption coefficient of lead (atomic number 82) for gamma rays, plotted versus gamma energy, and the contributions by the three effects. Here, the photoelectric effect dominates at low energy. Above 5 MeV, pair production starts to dominate.
  • VACIS]] (vehicle and container imaging system)
ELECTROMAGNETIC RADIATION OF HIGH FREQUENCY AND THEREFORE HIGH ENERGY
Gamma-ray; Gamma radiation; Gamma Ray; Gamma decay; Gamma particle; Gamma Radiation; Γ Radaition; Gamma particles; Gamma Rays; Gamma photon; Gamma Rays and their characteristics; Gamma-Ray; Gamma-rays; Gammaray; G Radaition; Gamma Ray Control; Gamma rays; Secondary radiation; Gamma-decay; Γ-ray; Γ-rays; Γ radiation; Gamma-ray source; Gamma-ray production; Gamma ray generation; Gamma ray production; Gamma-ray generation; Gamma emission; Γ ray; Y photons; Γ rays; Gamma-irradidated; Gamma-irradiated
A gamma ray, also known as gamma radiation (symbol γ or \gamma), is a penetrating form of electromagnetic radiation arising from the radioactive decay of atomic nuclei. It consists of the shortest wavelength electromagnetic waves, typically shorter than those of X-rays.
https://en.wikipedia.org/wiki/Gamma_ray
gamma rays         
  • Gamma emission spectrum of cobalt-60
  • The total absorption coefficient of aluminium (atomic number 13) for gamma rays, plotted versus gamma energy, and the contributions by the three effects. As is usual, the photoelectric effect is largest at low energies, Compton scattering dominates at intermediate energies, and pair production dominates at high energies.
  • Alpha radiation]] consists of [[helium]] nuclei and is readily stopped by a sheet of paper. [[Beta radiation]], consisting of [[electron]]s or [[positron]]s, is stopped by an aluminium plate, but gamma radiation requires shielding by dense material such as lead or concrete.
  • The red dots show some of the ~500 terrestrial gamma-ray flashes daily detected by the Fermi Gamma-ray Space Telescope through 2010. Credit: NASA/Goddard Space Flight Center.
  • 60}}
  • NASA guide to electromagnetic spectrum showing overlap of frequency between X-rays and gamma rays
  • In practice, gamma ray energies overlap with the range of X-rays, especially in the higher-frequency region referred to as "hard" X-rays. This depiction follows the older convention of distinguishing by wavelength.
  • Image of entire sky in 100 MeV or greater gamma rays as seen by the EGRET instrument aboard the [[CGRO]] spacecraft. Bright spots within the galactic plane are [[pulsar]]s while those above and below the plane are thought to be [[quasar]]s.
  • A [[hypernova]]. Artist's illustration showing the life of a [[massive star]] as [[nuclear fusion]] converts lighter elements into heavier ones. When fusion no longer generates enough pressure to counteract gravity, the star rapidly collapses to form a [[black hole]]. Theoretically, energy may be released during the collapse along the axis of rotation to form a long duration [[gamma-ray burst]].
  • access-date=2011-11-08}}</ref>
  • Fermi's]] Large Area Telescope (LAT).
  • The total absorption coefficient of lead (atomic number 82) for gamma rays, plotted versus gamma energy, and the contributions by the three effects. Here, the photoelectric effect dominates at low energy. Above 5 MeV, pair production starts to dominate.
  • VACIS]] (vehicle and container imaging system)
ELECTROMAGNETIC RADIATION OF HIGH FREQUENCY AND THEREFORE HIGH ENERGY
Gamma-ray; Gamma radiation; Gamma Ray; Gamma decay; Gamma particle; Gamma Radiation; Γ Radaition; Gamma particles; Gamma Rays; Gamma photon; Gamma Rays and their characteristics; Gamma-Ray; Gamma-rays; Gammaray; G Radaition; Gamma Ray Control; Gamma rays; Secondary radiation; Gamma-decay; Γ-ray; Γ-rays; Γ radiation; Gamma-ray source; Gamma-ray production; Gamma ray generation; Gamma ray production; Gamma-ray generation; Gamma emission; Γ ray; Y photons; Γ rays; Gamma-irradidated; Gamma-irradiated
Gamma rays are a type of electromagnetic radiation that has a shorter wavelength and higher energy than X-rays.
N-PLURAL
gamma rays         
  • Gamma emission spectrum of cobalt-60
  • The total absorption coefficient of aluminium (atomic number 13) for gamma rays, plotted versus gamma energy, and the contributions by the three effects. As is usual, the photoelectric effect is largest at low energies, Compton scattering dominates at intermediate energies, and pair production dominates at high energies.
  • Alpha radiation]] consists of [[helium]] nuclei and is readily stopped by a sheet of paper. [[Beta radiation]], consisting of [[electron]]s or [[positron]]s, is stopped by an aluminium plate, but gamma radiation requires shielding by dense material such as lead or concrete.
  • The red dots show some of the ~500 terrestrial gamma-ray flashes daily detected by the Fermi Gamma-ray Space Telescope through 2010. Credit: NASA/Goddard Space Flight Center.
  • 60}}
  • NASA guide to electromagnetic spectrum showing overlap of frequency between X-rays and gamma rays
  • In practice, gamma ray energies overlap with the range of X-rays, especially in the higher-frequency region referred to as "hard" X-rays. This depiction follows the older convention of distinguishing by wavelength.
  • Image of entire sky in 100 MeV or greater gamma rays as seen by the EGRET instrument aboard the [[CGRO]] spacecraft. Bright spots within the galactic plane are [[pulsar]]s while those above and below the plane are thought to be [[quasar]]s.
  • A [[hypernova]]. Artist's illustration showing the life of a [[massive star]] as [[nuclear fusion]] converts lighter elements into heavier ones. When fusion no longer generates enough pressure to counteract gravity, the star rapidly collapses to form a [[black hole]]. Theoretically, energy may be released during the collapse along the axis of rotation to form a long duration [[gamma-ray burst]].
  • access-date=2011-11-08}}</ref>
  • Fermi's]] Large Area Telescope (LAT).
  • The total absorption coefficient of lead (atomic number 82) for gamma rays, plotted versus gamma energy, and the contributions by the three effects. Here, the photoelectric effect dominates at low energy. Above 5 MeV, pair production starts to dominate.
  • VACIS]] (vehicle and container imaging system)
ELECTROMAGNETIC RADIATION OF HIGH FREQUENCY AND THEREFORE HIGH ENERGY
Gamma-ray; Gamma radiation; Gamma Ray; Gamma decay; Gamma particle; Gamma Radiation; Γ Radaition; Gamma particles; Gamma Rays; Gamma photon; Gamma Rays and their characteristics; Gamma-Ray; Gamma-rays; Gammaray; G Radaition; Gamma Ray Control; Gamma rays; Secondary radiation; Gamma-decay; Γ-ray; Γ-rays; Γ radiation; Gamma-ray source; Gamma-ray production; Gamma ray generation; Gamma ray production; Gamma-ray generation; Gamma emission; Γ ray; Y photons; Γ rays; Gamma-irradidated; Gamma-irradiated
(also gamma radiation)
¦ plural noun penetrating electromagnetic radiation of shorter wavelength than X-rays.
Gamma rays         
  • Gamma emission spectrum of cobalt-60
  • The total absorption coefficient of aluminium (atomic number 13) for gamma rays, plotted versus gamma energy, and the contributions by the three effects. As is usual, the photoelectric effect is largest at low energies, Compton scattering dominates at intermediate energies, and pair production dominates at high energies.
  • Alpha radiation]] consists of [[helium]] nuclei and is readily stopped by a sheet of paper. [[Beta radiation]], consisting of [[electron]]s or [[positron]]s, is stopped by an aluminium plate, but gamma radiation requires shielding by dense material such as lead or concrete.
  • The red dots show some of the ~500 terrestrial gamma-ray flashes daily detected by the Fermi Gamma-ray Space Telescope through 2010. Credit: NASA/Goddard Space Flight Center.
  • 60}}
  • NASA guide to electromagnetic spectrum showing overlap of frequency between X-rays and gamma rays
  • In practice, gamma ray energies overlap with the range of X-rays, especially in the higher-frequency region referred to as "hard" X-rays. This depiction follows the older convention of distinguishing by wavelength.
  • Image of entire sky in 100 MeV or greater gamma rays as seen by the EGRET instrument aboard the [[CGRO]] spacecraft. Bright spots within the galactic plane are [[pulsar]]s while those above and below the plane are thought to be [[quasar]]s.
  • A [[hypernova]]. Artist's illustration showing the life of a [[massive star]] as [[nuclear fusion]] converts lighter elements into heavier ones. When fusion no longer generates enough pressure to counteract gravity, the star rapidly collapses to form a [[black hole]]. Theoretically, energy may be released during the collapse along the axis of rotation to form a long duration [[gamma-ray burst]].
  • access-date=2011-11-08}}</ref>
  • Fermi's]] Large Area Telescope (LAT).
  • The total absorption coefficient of lead (atomic number 82) for gamma rays, plotted versus gamma energy, and the contributions by the three effects. Here, the photoelectric effect dominates at low energy. Above 5 MeV, pair production starts to dominate.
  • VACIS]] (vehicle and container imaging system)
ELECTROMAGNETIC RADIATION OF HIGH FREQUENCY AND THEREFORE HIGH ENERGY
Gamma-ray; Gamma radiation; Gamma Ray; Gamma decay; Gamma particle; Gamma Radiation; Γ Radaition; Gamma particles; Gamma Rays; Gamma photon; Gamma Rays and their characteristics; Gamma-Ray; Gamma-rays; Gammaray; G Radaition; Gamma Ray Control; Gamma rays; Secondary radiation; Gamma-decay; Γ-ray; Γ-rays; Γ radiation; Gamma-ray source; Gamma-ray production; Gamma ray generation; Gamma ray production; Gamma-ray generation; Gamma emission; Γ ray; Y photons; Γ rays; Gamma-irradidated; Gamma-irradiated
·add. ·- Very penetrating rays not appreciably deflected by a magnetic or electric field, emitted by radioactive substances. The prevailing view is that they are non-periodic ether pulses differing from Rontgen rays only in being more penetrating.
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