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A product involving an infinite number of terms. Such products can converge. In fact, for positive a_n, the product product_(n=1)^(infty)a_n converges to a nonzero number iff ...

The inverse tangent is the multivalued function tan^(-1)z (Zwillinger 1995, p. 465), also denoted arctanz (Abramowitz and Stegun 1972, p. 79; Harris and Stocker 1998, p. 311; ...

Two fractions are said to be adjacent if their difference has a unit numerator. For example, 1/3 and 1/4 are adjacent since 1/3-1/4=1/12, but 1/2 and 1/5 are not since ...

A sequence of circles which closes (such as a Steiner chain or the circles inscribed in the arbelos) is called a chain.

A linear operator A:D(A)->H from its domain D(A) into a Hilbert space H is closed if for any sequence of vectors v_n in D(A) such that v_n->v and Av_n->x as n->infty, it ...

Given a geometric sequence {a_1,a_1r,a_1r^2,...}, the number r is called the common ratio associated to the sequence.

A complete metric is a metric in which every Cauchy sequence is convergent. A topological space with a complete metric is called a complete metric space.

Suppose a,b in N, n=ab+1, and x_1, ..., x_n is a sequence of n real numbers. Then this sequence contains a monotonic increasing (decreasing) subsequence of a+1 terms or a ...

A periodic sequence such as {1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, ...} that is periodic from some point onwards.

The w-polynomials obtained by setting p(x)=3x and q(x)=-2 in the Lucas polynomial sequence. Setting f_n(1)=f_n (1) give a Fermat-Lucas number. The first few Fermat-Lucas ...