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Numerical Algorithms

, Volume 49, Issue 1–4, pp 153–157 | Cite as

The zeros of the complementary error function

  • Árpád Elbert
  • Andrea Laforgia
Original Paper
  • 63 Downloads

Abstract

We show that the complementary error function, \(\text{erfc} (z)= \frac{2}{\sqrt{\pi}}\int_z^{\infty}{e^{-s^2} \text{d}s}\), has no zeros in \(\text{D}= \left\{ z : \frac{3}{4} \ \pi \le Arg z \le\frac{5}{4} \ \pi \right\}\).

Keywords

Zeros Complementary error function 

Mathematics Subject Classification (2000)

Primary 33B20 

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References

  1. 1.
    Tricomi, F.G.: Funzioni ipergeometriche confluenti. Consiglio Nazionale delle Ricerche, Monografie Matematiche, 1, Edizioni Cremonese, Roma (1954)Google Scholar

Copyright information

© Springer Science+Business Media, LLC. 2008

Authors and Affiliations

  1. 1.Department of MathematicsRome Tre UniversityRomeItaly

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