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A graphical plot with abscissa given by the number p of consecutive numbers constituting a single period and ordinate given by the correlation ratio eta. The equation of the ...

Planck's's radiation function is the function f(x)=(15)/(pi^4)1/(x^5(e^(1/x)-1)), (1) which is normalized so that int_0^inftyf(x)dx=1. (2) However, the function is sometimes ...

Let n be a positive integer and r(n) the number of (not necessarily distinct) prime factors of n (with r(1)=0). Let O(m) be the number of positive integers <=m with an odd ...

The probability Q_delta that a random sample from an infinite normally distributed universe will have a mean m within a distance |delta| of the mean mu of the universe is ...

A technique for computing eigenfunctions and eigenvalues. It proceeds by requiring J=int_a^b[p(x)y_x^2-q(x)y^2]dx (1) to have a stationary value subject to the normalization ...

It is possible to describe a set of positive integers that cannot be listed in a book containing a set of counting numbers on each consecutively numbered page. Another form ...

A conformal mapping from the upper half-plane to a polygon.

Let p(n) be the first prime which follows a prime gap of n between consecutive primes. Shanks' conjecture holds that p(n)∼exp(sqrt(n)). Wolf conjectures a slightly different ...

The modification of a set of data to make it smooth and nearly continuous and remove or diminish outlying points.

Define the notation [n]f_0=f_(-(n-1)/2)+...+f_0+...+f_((n-1)/2) (1) and let delta be the central difference, so delta^2f_0=f_1-2f_0+f_(-1). (2) Spencer's 21-term moving ...