The notations , , , etc., as introduced by John Herschel in 1813, are often used as well in English-language sources, much more than the also established , , – conventions consistent with the notation of an inverse function, that is useful (for example) to define the multivalued version of each inverse trigonometric function: \tan^{-1}(x) = \{\arctan(x) + \pi k \mid k \in \mathbb Z\} ~. However, this might appear to conflict logically with the common semantics for expressions such as (although only , without parentheses, is the really common use), which refer to numeric power rather than function composition, and therefore may result in confusion between notation for the reciprocal (multiplicative inverse) and inverse function.
