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In mathematics, a functional square root (sometimes called a half iterate) is a square root of a function with respect to the operation of function composition. In other words, a functional square root of a function g is a function f satisfying f(f(x)) = g(x) for all x.
Notations expressing that f is a functional square root of g are f = g[1/2] and f = g1/2.[ citation needed]
A systematic procedure to produce arbitrary functional n-roots (including arbitrary real, negative, and infinitesimal n) of functions relies on the solutions of Schröder's equation. [3] [4] [5] Infinitely many trivial solutions exist when the domain of a root function f is allowed to be sufficiently larger than that of g.
(See. [6] For the notation, see [1] Archived 2022-12-05 at the Wayback Machine.)
![]() | This article needs editing to comply with Wikipedia's
Manual of Style. In particular, it has problems with
MOS:RADICAL. (June 2022) |
In mathematics, a functional square root (sometimes called a half iterate) is a square root of a function with respect to the operation of function composition. In other words, a functional square root of a function g is a function f satisfying f(f(x)) = g(x) for all x.
Notations expressing that f is a functional square root of g are f = g[1/2] and f = g1/2.[ citation needed]
A systematic procedure to produce arbitrary functional n-roots (including arbitrary real, negative, and infinitesimal n) of functions relies on the solutions of Schröder's equation. [3] [4] [5] Infinitely many trivial solutions exist when the domain of a root function f is allowed to be sufficiently larger than that of g.
(See. [6] For the notation, see [1] Archived 2022-12-05 at the Wayback Machine.)