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A gamma-ray spectrometer (GRS) is an instrument for measuring the distribution (or spectrum—see figure) of the intensity of gamma radiation versus the energy of each photon. The study and analysis of gamma-ray spectra for scientific and technical use is called gamma spectroscopy , and gamma-ray spectrometers are the instruments which observe ...
A detailed analysis of this spectrum is typically used to determine the identity and quantity of gamma emitters present in a gamma source, and is a vital tool in radiometric assay. The gamma spectrum is characteristic of the gamma-emitting nuclides contained in the source, just like in an optical spectrometer , the optical spectrum is ...
One of the advantage of defining this type incomplete-version of Bessel function (,) is that even for example the associated Anger–Weber function defined in Digital Library of Mathematical Functions [6] can related:
Interpolated approximations and bounds are all of the form ~ () + (~ ()) where ~ is an interpolating function running monotonially from 0 at low α to 1 at high α, approximating an ideal, or exact, interpolator (): = () () For the simplest interpolating function considered, a first-order rational function ~ = + the tightest lower bound has ...
File:Gamma_distribution_pdf.png licensed with Cc-by-sa-3.0-migrated, GFDL, GPL 2005-03-10T20:34:05Z MarkSweep 1300x975 (162472 Bytes) new version of PDF and matching CDF; 2005-03-10T17:45:44Z Cburnett 960x720 (138413 Bytes) Probability density function for the Gamma distribution {{GFDL}} Uploaded with derivativeFX
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 ...
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In the implementation of the pulse-shape analysis technique for AGATA, the measured pulse shapes are compared, in real time, to the database of signals calculated on a fine (2 mm) grid for each type of AGATA HPGe crystals [1] The calculations have been validated by comparisons with pulses measured using tightly collimated γ-ray sources. [1]