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...

mathematics, a square root 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...

distribution of a function of a random variable Functional decomposition Functional square root Functional equation Higher-order function Infinite compositions...

In mathematics, a half-exponential function is a functional square root of an exponential function. That is, a function f {\displaystyle f} such that f...

group active from 2003 to 2009 rin(), one representation of the functional square root of sin() Rin (album) (凛, "Dignified") 2017 Rin, an English language...

{\sqrt {D}}=D^{\scriptstyle {\frac {1}{2}}}} as an analogue of the functional square root for the differentiation operator, that is, an expression for some...

equation Functional square root Abel function Böttcher's equation Infinite compositions of analytic functions Flow (mathematics) Tetration Functional equation...

Square root algorithms compute the non-negative square root S {\displaystyle {\sqrt {S}}} of a positive real number S {\displaystyle S} . Since all square...

mathematics, the square root of a matrix extends the notion of square root from numbers to matrices. A matrix B is said to be a square root of A if the matrix...

exponential; on the base of this Abel function, he constructed the functional square root of the exponential function as a half-iteration of the exponential...

by abuse of notation, since it is not straightforward to take a functional square root of the sum of two differential operators) take the relativistic...

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...

In geometry, the spiral of Theodorus (also called the square root spiral, Pythagorean spiral, or Pythagoras's snail) is a spiral composed of right triangles...

polynomial functions to a square matrix, extending what has just been discussed. In the finite-dimensional case, the polynomial functional calculus yields quite...

been constructed; in effect, the entire orbit. For instance, the functional square root is h1/2(x) = Ψ−1(s1/2 Ψ(x)), so that h1/2(h1/2(x)) = h(x), and so...

exist as well, for example, in the case of the square root, a horizontal bar extending the square root sign over the argument can indicate the extent...

theory determining cases where a Gauss sum is the square root of a prime number, multiplied by a root of unity. It was proved and published independently...

Completing the square Abel–Ruffini theorem Bring radical Binomial theorem Blossom (functional) Root of a function nth root (radical) Surd Square root Methods...

the magnitude or length of the vector. This norm can be defined as the square root of the inner product of a vector with itself. A seminorm satisfies the...

The two squared formulas inside the square root give the areas of squares on the horizontal and vertical sides, and the outer square root converts the...

all other strategies". By analogy with the square root of x, one can define the (positive) triangular root of x as the number n such that Tn = x: n =...

_{y}x} Like square roots, the square super-root of x may not have a single solution. Unlike square roots, determining the number of square super-roots...

them at least. Another generalization is Newton's method to find a root of a functional F defined in a Banach space. In this case the formulation is X n...

the domain of the square root function, along a path of complex numbers with positive imaginary parts, one gets i for the square root of −1; while, when...

In functional programming, monads are a way to structure computations as a sequence of steps, where each step not only produces a value but also some extra...

goodness of fit. The norm of residuals is calculated as the square-root of the sum of squares of residuals (SSR): norm of residuals = S S res = ‖ e ‖ ....

Least-squares spectral analysis Measurement uncertainty Orthogonal projection Proximal gradient methods for learning Quadratic loss function Root mean...

mesial, while the occlusal table remains squared. Viewed from the buccal the buccal cusp is centered over the root as in the three cusp variety. Viewed from...

distance by a factor of 1.4 (the square root of 2), and to double illumination, reduce the distance to 0.7 (square root of 1/2). When the illuminant is...

the problem in 1953. Kato asked whether the square roots of certain elliptic operators, defined via functional calculus, are analytic. The full statement...