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In mathematics, the super-logarithm (or tetra-logarithm〔http://oeis.org/wiki/Tetra-logarithms〕) is one of the two inverse functions of tetration. Just as exponentiation has two inverse functions, roots and logarithms, tetration has two inverse functions, super-roots and super-logarithms. There are several ways of interpreting super-logarithms: * As the Abel function of exponential functions, * As the inverse function of tetration with respect to the height, * As the number of times a logarithm must be iterated to get to 1 (the Iterated logarithm), * As a generalization of Robert Munafo's (large number class system ), The precise definition of the super-logarithm depends on a precise definition of non-integral tetration (that is, for ''y'' not an integer). There is no clear consensus on the definition of non-integral tetration and so there is likewise no clear consensus on the super-logarithm for non-integer range. ==Definitions== The super-logarithm, written , is defined implicitly by : and : Notice that this definition can only have integer outputs, and will only accept values that will produce integer outputs. The only numbers that this definition will accept are of the form and so on. In order to extend the domain of the super-logarithm from this sparse set to the real numbers, several approaches have been pursued. These usually include a third requirement in addition to those listed above, which vary from author to author. These approaches are as follows: * The linear approximation approach by Rubstov and Romerio, * The quadratic approximation approach by Andrew Robbins, * The regular Abel function approach by George Szekeres, * The iterative functional approach by Peter Walker, and * The natural matrix approach by Peter Walker, and later generalized by Andrew Robbins. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Super-logarithm」の詳細全文を読む スポンサード リンク
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