Search Results for ""

A branch of mathematics that is a sort of generalization of calculus. Calculus of variations seeks to find the path, curve, surface, etc., for which a given function has a ...

For R[mu+nu]>1, int_(-pi/2)^(pi/2)cos^(mu+nu-2)thetae^(itheta(mu-nu+2xi))dtheta=(piGamma(mu+nu-1))/(2^(mu+nu-2)Gamma(mu+xi)Gamma(nu-xi)), where Gamma(z) is the gamma function.

The term "characteristic" has many different uses in mathematics. In general, it refers to some property that inherently describes a given mathematical object, for example ...

A confidence interval is an interval in which a measurement or trial falls corresponding to a given probability. Usually, the confidence interval of interest is symmetrically ...

Differential entropy differs from normal or absolute entropy in that the random variable need not be discrete. Given a continuous random variable X with a probability density ...

A notation invented by Dirac which is very useful in quantum mechanics. The notation defines the "ket" vector, denoted |psi>, and its conjugate transpose, called the "bra" ...

The continuous Fourier transform is defined as f(nu) = F_t[f(t)](nu) (1) = int_(-infty)^inftyf(t)e^(-2piinut)dt. (2) Now consider generalization to the case of a discrete ...

Ellipsoidal harmonics of the second kind, also known as Lamé functions of the second kind, are variously defined as F_m^p(x)=(2m+1)E_m^p(x) ...

Consider a first-order ODE in the slightly different form p(x,y)dx+q(x,y)dy=0. (1) Such an equation is said to be exact if (partialp)/(partialy)=(partialq)/(partialx). (2) ...

In the most commonly used convention (e.g., Apostol 1967, pp. 202-204), the first fundamental theorem of calculus, also termed "the fundamental theorem, part I" (e.g., Sisson ...