Guide alphabétique, de la thermodynamique, amplification de chaleur, transfert de masse, et dynamique des fluides
Français English Русский 中文 Português Español Deutsch À propos Comité de rédaction Contactez-nous Accès Begell House
View in A-Z Index

An error function is defined by the integral

(1)

and it occurs frequently in engineering problems; e.g., in heat conduction problems. The error function represents the area under the Gaussian function from t = 0 to t = x, so that erf ∞ = 1. The complementary error function is:

(2)

The error function erf x is a monotonically increasing odd function of x; i.e., erf (–x) = –erf x and erf x1 ≤ erf x2 whenever x1 ≤ x2. Its Maclaurin series (for small x) is given by:

(3)

and for large values of x, the asymptotic expansion is:

(4)

where erf x may be approximated as

(5)

There exist extensive tabulations of erf x [see Abramowitz and Stegun (1965), for example].

REFERENCES

Abramowitz, M. and Stegun, I. (1965) Handbook of Mathematical Functions, Dover Publications, New York.

References

  1. Abramowitz, M. and Stegun, I. (1965) Handbook of Mathematical Functions, Dover Publications, New York. DOI: 10.1119/1.1972842
Nombre de vues : 32310 Article ajouté : 2 February 2011 Dernière modification de l'article : 11 February 2011 © Copyright 2010-2022 Retour en haut de page
Index A-Z Auteur / Rédacteurs Carte sémantique Galerie visuelle Contribuez Guest