Function that, applied twice, gives another function
Not to be confused with Root of a function.
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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.
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In mathematics, a functionalsquareroot (sometimes called a half iterate) is a squareroot of a function with respect to the operation of function composition...
mathematics, a squareroot of a number x is a number y such that y 2 = x {\displaystyle y^{2}=x} ; in other words, a number y whose square (the result of...
variable, distribution of a function of a random variable Functional decomposition Functionalsquareroot Higher-order function Infinite compositions of analytic...
mathematics, the squareroot of a matrix extends the notion of squareroot from numbers to matrices. A matrix B is said to be a squareroot of A if the matrix...
group active from 2003 to 2009 rin(), one representation of the functionalsquareroot of sin() Rin (album) (凛, "Dignified") 2017 Rin, an English language...
Methods of computing square roots are algorithms for approximating the non-negative squareroot S {\displaystyle {\sqrt {S}}} of a positive real number...
{\sqrt {D}}=D^{\scriptstyle {\frac {1}{2}}}} as an analogue of the functionalsquareroot for the differentiation operator, that is, an expression for some...
In geometry, the spiral of Theodorus (also called the squareroot spiral, Pythagorean spiral, or Pythagoras's snail) is a spiral composed of right triangles...
exponential; on the base of this Abel function, he constructed the functionalsquareroot of the exponential function as a half-iteration of the exponential...
efficiently. Generate a random number, square it modulo n, and have the efficient squareroot algorithm find a root. Repeat until it returns a number not...
instance if T is an operator, applying the squaring function s → s2 to T yields the operator T2. Using the functional calculus for larger classes of functions...
polynomial functions to a square matrix, extending what has just been discussed. In the finite-dimensional case, the polynomial functional calculus yields quite...
The two squared formulas inside the squareroot give the areas of squares on the horizontal and vertical sides, and the outer squareroot converts the...
optimal trial division algorithm uses all prime numbers not exceeding its squareroot, whereas the sieve of Eratosthenes produces each composite from its prime...
numbers is a square number, with the sum being the square of the difference between the two (and thus the difference of the two being the squareroot of the...
indicating goodness of fit. This term is calculated as the square-root of the sum of squares of residuals: norm of residuals = S S res = ‖ e ‖ . {\displaystyle...
statistical population, data set, or probability distribution is the squareroot of its variance. It is algebraically simpler, though in practice less...
or "name". It was derived from the term binomial by replacing the Latin root bi- with the Greek poly-. That is, it means a sum of many terms (many monomials)...
approximate the squareroot of a number is to use the following equation: root ≃ known squareroot − known square − unknown square 2 × known squareroot {\displaystyle...
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