An Integral which arises in computation of the Voigt lineshape:

(1) |

(2) |

(3) | |||

(4) |

where is the Erf function and is the imaginary error function Erfi. is illustrated in the left figure above, and in the right figure. has a maximum at , or

(5) |

(6) |

(7) |

(8) |

**References**

Abramowitz, M. and Stegun, C. A. (Eds.).
*Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.*
New York: Dover, p. 298, 1972.

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. ``Dawson's Integrals.'' §6.10 in
*Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed.* Cambridge, England:
Cambridge University Press, pp. 252-254, 1992.

Spanier, J. and Oldham, K. B. ``Dawson's Integral.''
Ch. 42 in *An Atlas of Functions.* Washington, DC: Hemisphere, pp. 405-410, 1987.

© 1996-9

1999-05-24