Half-exponential function: Difference between revisions

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In mathematics, a '''half-exponential function''' is a function ''&fnof;'' so that if ''&fnof;'' is composed with itself the result is exponential:<ref name="miltersensqrtexp">{{cite journal |author=Peter Bro Miltersen, N. V. Vinodchandran, 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}}</ref>

|author=Kneser, H. |authorlink=Hellmuth Kneser

|title=Reelle analytische Lösungen der Gleichung ''&phi;''(''&phi;''(''x''))&nbsp;=&nbsp;''e''^''x'' und verwandter Funktionalgleichungen

|journal=[[Journal fur die reine und angewandte Mathematik]]

|url=http://resolver.sub.uni-goettingen.de/purl?GDZPPN002175851

|volume=187

|year=1950

|pages=56&ndash;67}}

</ref> <ref name="miltersen">{{cite journal |author=Peter Bro Miltersen, N. V. Vinodchandran, 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}}</ref>

: <math> f(f(x)) = ab^x. \, </math>