Search results
Results from the WOW.Com Content Network
The slope field of () = +, showing three of the infinitely many solutions that can be produced by varying the arbitrary constant c.. In calculus, an antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral [Note 1] of a continuous function f is a differentiable function F whose derivative is equal to the original function f.
This is the case, for example, if f(x) = x 3 − 2x + 2. For this function, it is even the case that Newton's iteration as initialized sufficiently close to 0 or 1 will asymptotically oscillate between these values. For example, Newton's method as initialized at 0.99 yields iterates 0.99, −0.06317, 1.00628, 0.03651, 1.00196, 0.01162, 1.00020 ...
Risch called it a decision procedure, because it is a method for deciding whether a function has an elementary function as an indefinite integral, and if it does, for determining that indefinite integral. However, the algorithm does not always succeed in identifying whether or not the antiderivative of a given function in fact can be expressed ...
In mathematics, a nonelementary antiderivative of a given elementary function is an antiderivative (or indefinite integral) that is, itself, not an elementary function. [1] A theorem by Liouville in 1835 provided the first proof that nonelementary antiderivatives exist. [ 2 ]
In complex analysis, a branch of mathematics, the antiderivative, or primitive, of a complex-valued function g is a function whose complex derivative is g.More precisely, given an open set in the complex plane and a function :, the antiderivative of is a function : that satisfies =.
So this type of estimation is called confidence interval estimation. [2] This estimation provides a range of values which the parameter is expected to lie. It generally gives more information than point estimates and are preferred when making inferences. In some way, we can say that point estimation is the opposite of interval estimation.
Sigmoid curves are also common in statistics as cumulative distribution functions (which go from 0 to 1), such as the integrals of the logistic density, the normal density, and Student's t probability density functions. The logistic sigmoid function is invertible, and its inverse is the logit function.
As defined by Theil (1950), the Theil–Sen estimator of a set of two-dimensional points (x i, y i) is the median m of the slopes (y j − y i)/(x j − x i) determined by all pairs of sample points. Sen (1968) extended this definition to handle the case in which two data points have the same x coordinate.