Search Results for ""

The chi distribution with n degrees of freedom is the distribution followed by the square root of a chi-squared random variable. For n=1, the chi distribution is a ...

A generalized Vandermonde matrix of two sequences a and b where a is an increasing sequence of positive integers and b is an increasing sequence of nonnegative integers of ...

The Bernoulli distribution is a discrete distribution having two possible outcomes labelled by n=0 and n=1 in which n=1 ("success") occurs with probability p and n=0 ...

The generalized law of sines applies to a simplex in space of any dimension with constant Gaussian curvature. Let us work up to that. Initially in two-dimensional space, we ...

A generalization of the polylogarithm function defined by S_(n,p)(z)=((-1)^(n+p-1))/((n-1)!p!)int_0^1((lnt)^(n-1)[ln(1-zt)]^p)/tdt. The function reduces to the usual ...

The generalized Riemann hypothesis conjectures that neither the Riemann zeta function nor any Dirichlet L-series has a zero with real part larger than 1/2. Compare with ...

The triangular distribution is a continuous distribution defined on the range x in [a,b] with probability density function P(x)={(2(x-a))/((b-a)(c-a)) for a<=x<=c; ...

The ratio X_1/X_2 of uniform variates X_1 and X_2 on the interval [0,1] can be found directly as P_(X_1/X_2)(u) = int_0^1int_0^1delta((x_1)/(x_2)-u)dx_1dx_2 (1) = ...

A generalized Fourier series is a series expansion of a function based on the special properties of a complete orthogonal system of functions. The prototypical example of ...

In 1757, V. Riccati first recorded the generalizations of the hyperbolic functions defined by F_(n,r)^alpha(x)=sum_(k=0)^infty(alpha^k)/((nk+r)!)x^(nk+r), (1) for r=0, ..., ...