Half-exponential function: Difference between revisions

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In [[mathematics]], a '''half-exponential function''' is a [[functional square root]] of an [[exponential function]], that is, a [[function (mathematics)|function]] <math>f</math> that, if [[function composition|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 {{math|''&phi;φ''(''&phi;φ''(''x''))&nbsp; {{=&nbsp;}} ''e''^''x''}} und verwandter Funktionalgleichungen

|journal=[[Crelle's Journal|Journal für die reine und angewandte Mathematik]]

|url=httphttps://resolvergdz.sub.uni-goettingen.de/purlid/PPN243919689_0187?GDZPPN002175851tify={"pages":[62]}

|volume=187

|year=19501949|mr=0035385

|pages=56&ndash;67}}

</ref><ref name="miltersen">{{cite book |author1=Peter Bro Miltersen |author2=N. V. Vinodchandran |author3=Osamu Watanabe |title=Super-Polynomial Versus Half-Exponential Circuit Size in the Exponential Hierarchy |journal=Lecture Notes in Computer Science |volume=1627 |year=1999 |pages=210–220 |doi=10.1007/3-540-48686-0_21|isbn=978-3-540-66200-6 |citeseerx=10.1.1.16.2908 }}</ref>