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

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Di Rocco H., Aguirre Téllez M.

Acta Physica Polonica A

2004

vol. 106

issue 6

817-826

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.

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1 Acta Physica Polonica A

1 2004

1 Aguirre Téllez M.

1 Di Rocco H.

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