Search Results for ""

A positive value of n for which x-phi(x)=n has no solution, where phi(x) is the totient function. The first few are 10, 26, 34, 50, 52, ... (OEIS A005278).

A positive even value of n for which phi(x)=n, where phi(x) is the totient function, has no solution. The first few are 14, 26, 34, 38, 50, ... (OEIS A005277).

The nth raw moment mu_n^' (i.e., moment about zero) of a distribution P(x) is defined by mu_n^'=<x^n>, (1) where <f(x)>={sumf(x)P(x) discrete distribution; intf(x)P(x)dx ...

The hyperfactorial (Sloane and Plouffe 1995) is the function defined by H(n) = K(n+1) (1) = product_(k=1)^(n)k^k, (2) where K(n) is the K-function. The hyperfactorial is ...

There are infinitely many primes m which divide some value of the partition function P.

In accounting, the principal is the original amount borrowed or lent on which interest is then paid or given. The word "principal" is also used in many areas of mathematics ...

The sum of the absolute squares of the spherical harmonics Y_l^m(theta,phi) over all values of m is sum_(m=-l)^l|Y_l^m(theta,phi)|^2=(2l+1)/(4pi). (1) The double sum over m ...

A variable is a symbol on whose value a function, polynomial, etc., depends. For example, the variables in the function f(x,y) are x and y. A function having a single ...

An integral of the form intf(z)dz, (1) i.e., without upper and lower limits, also called an antiderivative. The first fundamental theorem of calculus allows definite ...

The vertical line test is a graphical method of determining whether a curve in the plane represents the graph of a function by visually examining the number of intersections ...