Erfc Differential Equation

The second-order ordinary differential equation

(1)

whose solutions may be written either

(2)

where  is the repeated integral of the erfc function (Abramowitz and Stegun 1972, p. 299), or

(3)

where  is a Hermite polynomial and  is a confluent hypergeometric function of the first kind.

REFERENCES:

Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 299, 1972.

Zwillinger, D. Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, p. 122, 1997.