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The product logarithm Lambert W function plotted in the complex plane from −2 − 2i to 2 + 2i The graph of y = W(x) for real x < 6 and y > −4.The upper branch (blue) with y ≥ −1 is the graph of the function W 0 (principal branch), the lower branch (magenta) with y ≤ −1 is the graph of the function W −1.
Inverse hyperbolic functions. The hyperbolic functions sinh, cosh, and tanh with respect to a unit hyperbola are analogous to circular functions sin, cos, tan with respect to a unit circle. The argument to the hyperbolic functions is a hyperbolic angle measure. In mathematics, the inverse hyperbolic functions are inverses of the hyperbolic ...
Such complex logarithm functions are analogous to the real logarithm function: >, which is the inverse of the real exponential function and hence satisfies e ln x = x for all positive real numbers x. Complex logarithm functions can be constructed by explicit formulas involving real-valued functions, by integration of 1 / z {\displaystyle 1/z ...
In mathematics, the logarithm is the inverse function to exponentiation. That means that the logarithm of a number x to the base b is the exponent to which b must be raised to produce x. For example, since 1000 = 103, the logarithm base of 1000 is 3, or log10 (1000) = 3.
Mathematically, the probit is the inverse of the cumulative distribution function of the standard normal distribution, which is denoted as , so the probit is defined as. . Largely because of the central limit theorem, the standard normal distribution plays a fundamental role in probability theory and statistics.
Logit. Plot of logit ( x) in the domain of 0 to 1, where the base of the logarithm is e. In statistics, the logit ( / ˈloʊdʒɪt / LOH-jit) function is the quantile function associated with the standard logistic distribution. It has many uses in data analysis and machine learning, especially in data transformations .
Inverse Gaussian. In probability theory, the inverse Gaussian distribution (also known as the Wald distribution) is a two-parameter family of continuous probability distributions with support on (0,∞). Its probability density function is given by. for x > 0, where is the mean and is the shape parameter.
A function f and its inverse f −1. Because f maps a to 3, the inverse f −1 maps 3 back to a. In mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective, and if it exists, is denoted by.