Evaluation of the Asymmetric Voigt Profile and Complex Error Functions in Terms of the Kummer Functions |
H.O. Di Rocco and M. Aguirre Téllez
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 |
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Received: 16 08 2004; in final form: 19 10 2004; |
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,a2). 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. |
DOI: 10.12693/APhysPolA.106.817 PACS numbers: 32.70.Jz, 33.70.Jg, 34.20.Cf |