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→See also: add gamma function |
m →Formulation: WL |
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For the alternative convention that {{math|''H''(0) {{=}} {{sfrac|1|2}}}}, it may be expressed as:
* a [[linear transformation]] of the [[sign function]], <math display="block">H(x) := \frac{1}{2} \left(\mbox{sgn}\, x + 1\right)</math>
* the [[arithmetic mean]] of two [[Iverson bracket]]s, <math display="block">H(x) := \frac{[x\geq 0] + [x>0]}{2}</math>
* a [[one-sided limit]] of the [[atan2|two-argument arctangent]] <math display="block">H(x) =: \lim_{\epsilon\to0^{+}} \frac{\mbox{atan2}(\epsilon,-x)}{\pi}</math>
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