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A generalization of the Wilcoxon rank sum test.

Given a series of positive terms u_i and a sequence of finite positive constants a_i, let rho=lim_(n->infty)(a_n(u_n)/(u_(n+1))-a_(n+1)). 1. If rho>0, the series converges. ...

Given an arithmetic progression of terms an+b, for n=1, 2, ..., the series contains an infinite number of primes if a and b are relatively prime, i.e., (a,b)=1. This result ...

The Dirichlet lambda function lambda(x) is the Dirichlet L-series defined by lambda(x) = sum_(n=0)^(infty)1/((2n+1)^x) (1) = (1-2^(-x))zeta(x), (2) where zeta(x) is the ...

Dirichlet's principle, also known as Thomson's principle, states that there exists a function u that minimizes the functional D[u]=int_Omega|del u|^2dV (called the Dirichlet ...

A nonparametric alternative to the two-sample t-test.

A test for determining the probability that a given result could not have occurred by chance (its significance).

The limit test, also sometimes known as the nth term test, says that if lima_n!=0 or this limit does not exist as n tends to infinity, then the series suma_n does not ...

A statistical test in which assumptions are made about the underlying distribution of observed data.

The Wilcoxon test statistic is equivalent to the T_+ statistic in the Wilcoxon signed rank test (Kanji 1999).