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2004 | 106 | 6 | 817-826
Article title

Evaluation of the Asymmetric Voigt Profile and Complex Error Functions in Terms of the Kummer Functions

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Languages of publication
EN
Abstracts
EN
In this work we present the explicit representations of the Voigt function K(a,b) (the convolution between a Gaussian and a Lorentzian function), the function N(a,b) defined as the convolution of Gaussian and dispersion distributions as well as the complex error function erf(a+ib), all in terms of the Kummer functions M(α,γ,a^2). The expansions are valid for all values of the parameter a (the relation between Lorentzian and Gaussian widths at the half maxima). Previous analytical works were known only when the parameter a≤1, or were based on numerical interpolations or empirical approximations. Also, new series and asymptotic expansions are presented.
Keywords
EN
Publisher

Year
Volume
106
Issue
6
Pages
817-826
Physical description
Dates
published
2004-12
received
2004-08-16
(unknown)
2004-10-19
Contributors
author
  • Instituto de Fì sica Arroyo Seco and Núcleo de Matemática Pura y Aplicada, Facultad de Ciencias Exactas, Universidad Nacional del Centro, Pinto 399, 7000 Tandil, Argentina
  • Instituto de Fì sica Arroyo Seco and Núcleo de Matemática Pura y Aplicada, Facultad de Ciencias Exactas, Universidad Nacional del Centro, Pinto 399, 7000 Tandil, Argentina
References
  • 1. R. Ciurylo, J. Domyslawska, R.S. Trawinski, Acta Phys. Pol. A, 83, 425, 1993
  • 2. A.E. Siegman, Lasers, 2nd. ed., University Science, Mil Valley, California 1986
  • 3. W.J. Thompson, Comput. in Phys., 7, 627, 1993
  • 4. R.J. Wells, J. Quant. Spectrosc. Radiat. Transf., 62, 29, 1999
  • 5. M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions, Dover Publications, New York 1968
  • 6. A. Erdelyi, W. Magnus, F. Oberhettinger, F.G. Tricomi, Higher Transcendental Functions, Vol. 2, McGraw-Hill, New York 1953
  • 7. S.M. Smirnov, A Course of Higher Mathematics, Pergamon Press, Oxford 1964 (translated from Russian)
  • 8. I.S. Gradstein, I.M. Ryzhik, Table of Integrals, Series and Products, 5th ed., Academic Press, San Diego 1994
  • 9. D. Mihalas, Stellar Atmospheres, 2nd. ed., W.H. Freeman, San Francisco 1982
  • 10. W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes, 2nd. ed. Cambridge University Press, Cambridge 1992
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.bwnjournal-article-appv106n602kz
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