## Dawson's Integral

An Integral which arises in computation of the Voigt lineshape:

 (1)

It is sometimes generalized such that
 (2)

giving
 (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)

giving
 (6)

and an inflection at , or
 (7)

giving
 (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.