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In mathematics, a '''half-exponential function''' is a function ''ƒ'' that, if composed with itself, results in an [[exponential function]]:<ref name="sqrtexp">{{cite journal
|author=Kneser, H. |authorlink=Hellmuth Kneser
|title=Reelle analytische Lösungen der Gleichung ''φ''(''φ''(''x'')) = ''e''<sup>''x''</sup> und verwandter Funktionalgleichungen
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