A-Z-Leitfaden über Thermodynamik, Wärme- und Stoffübertragung und Strömungstechnik
Deutsch English Русский 中文 Português Español Français Über unser Angebot Redaktion Kontakt Zugriff Begell House
View in A-Z Index
Anzahl der Aufrufe:
32904

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
Zurück nach oben © Copyright 2010-2022
A-Z-Index Autoren / Redakteure Semantische Karte Visuelle Galerie Einen Beitrag leisten Guest