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If r experiments are performed with n_i possible outcomes for each experiment i=1,2,...,r, then there are a total of product_(i=1)^(r)n_i possible outcomes.

A sequence of primes q_1<q_2<...<q_k is a Cunningham chain of the first kind (second kind) of length k if q_(i+1)=2q_i+1 (q_(i+1)=2q_i-1) for i=1, ..., k-1. Cunningham primes ...

A diafix of a string T=s_1s_2...s_N is a substring s_(i+1)...s_(N-i) (0<=i<N/2). It is therefore not a first (prefix) or last (suffix) part of a string, but rather is a ...

The Dirichlet kernel D_n^M is obtained by integrating the number theoretic character e^(i<xi,x>) over the ball |xi|<=M, D_n^M=-1/(2pir)d/(dr)D_(n-2)^M.

A dual number is a number x+epsilony, where x,y in R and epsilon is a matrix with the property that epsilon^2=0 (such as epsilon=[0 1; 0 0]).

Legendre and Whittaker and Watson's (1990) term for the beta integral int_0^1x^p(1-x)^qdx, whose solution is the beta function B(p+1,q+1).

A sequence {a_1,a_2,a_3,...} fulfils a given property eventually if it fulfils it from some point onward, or, more precisely, if the property is fulfilled by the subsequence ...

A 1-form w is said to be exact in a region R if there is a function f that is defined and of class C^1 (i.e., is once continuously differentiable in R) and such that df=w.

The primes with Legendre symbol (n/p)=1 (less than N=pi(d) for trial divisor d) which need be considered when using the quadratic sieve factorization method.

Euler (1738, 1753) considered the series s_a(x)=sum_(n=1)^infty[1/(1-a^n)product_(k=0)^(n-1)(1-xa^(-k))]. He showed that just like log_a(a^n)=n, s_a(a^n)=n for nonnegative ...