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 \(\text{D}= \left\{ z : \frac{3}{4} \ \pi \le Arg z \le\frac{5}{4} \ \pi \right\}\).
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Tricomi, F.G.: Funzioni ipergeometriche confluenti. Consiglio Nazionale delle Ricerche, Monografie Matematiche, 1, Edizioni Cremonese, Roma (1954)
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Árpád Elbert deceased on April 25, 2001. The second Author started the research object of the present paper with Árpád, in May 1999 and only now he was able to give a complete proof of the results.
In the memory of Luigi Gatteschi.
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Elbert, Á., Laforgia, A. The zeros of the complementary error function. Numer Algor 49, 153–157 (2008). https://doi.org/10.1007/s11075-008-9186-7
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DOI: https://doi.org/10.1007/s11075-008-9186-7