Complementary Error Function of Zero
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Theorem
- $\map \erfc 0 = 1$
where $\erfc$ denotes the complementary error function.
Proof
\(\ds \map \erfc 0\) | \(=\) | \(\ds 1 - \map \erf 0\) | Definition of Complementary Error Function | |||||||||||
\(\ds \) | \(=\) | \(\ds 1\) | Error Function of Zero |
$\blacksquare$
Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 35$: Complementary Error Function $\ds \map \erfc x = 1 - \map \erf x = \frac 2 {\sqrt \pi} \int_x^\infty e^{-u^2} \rd u$: $35.6$