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Analytical Evaluation of the Plasma Dispersion Function Using Binomial Coefficients and Incomplete Gamma Functions
Author(s) -
Mamedov B.A.
Publication year - 2009
Publication title -
contributions to plasma physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.531
H-Index - 47
eISSN - 1521-3986
pISSN - 0863-1042
DOI - 10.1002/ctpp.200910006
Subject(s) - series (stratigraphy) , binomial coefficient , gamma function , dispersion (optics) , function (biology) , plasma , representation (politics) , binomial theorem , negative binomial distribution , mathematics , statistical physics , range (aeronautics) , dispersion relation , incomplete gamma function , physics , mathematical analysis , statistics , materials science , quantum mechanics , combinatorics , paleontology , evolutionary biology , politics , political science , law , composite material , poisson distribution , biology
Series expansions are obtained for a plasma dispersion function that appears in the description of smallamplitude waves in very hot plasmas. However, the numerical implementation of this function is required in diverse areas of physics and applied mathematics. An explicit representation for the plasma dispersion function is developed in terms of series of binomial coefficients and incomplete gamma functions. The series expansions obtained herein give a more accurate and efficient way to compute values for this integral over the entire permissible range of its parameters. The results of the calculations are compared with literature data as well as those obtained by different approximate method (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)