Half-exponential function: Difference between revisions

Revision as of 05:26, 18 May 2022

Revision as of 02:10, 14 September 2022

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for some constants {{nowrap|<math>a</math> and <math>b</math>.}}

==Impossibility of a closed -form formula==

If a function <math>f</math> is defined using the standard arithmetic operations, exponentials, [[logarithm]]s, and [[Real number|real]]-valued constants, then <math>f\bigl(f(x)\bigr)</math> is either subexponential or superexponential.{{r|transseries}} Thus, a [[Hardy field#Examples|Hardy {{mvar|L}}-function]] cannot be half-exponential.

==Construction==