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The alternating harmonic series is the series sum_(k=1)^infty((-1)^(k-1))/k=ln2, which is the special case eta(1) of the Dirichlet eta function eta(z) and also the x=1 case ...

The surface with parametric equations x = (sinhvcos(tauu))/(1+coshucoshv) (1) y = (sinhvsin(tauu))/(1+coshucoshv) (2) z = (coshvsinh(u))/(1+coshucoshv), (3) where tau is the ...

Two matrices A and B are said to be equal iff a_(ij)=b_(ij) (1) for all i,j. Therefore, [1 2; 3 4]=[1 2; 3 4], (2) while [1 2; 3 4]!=[0 2; 3 4]. (3)

Defined for samples x_i, i=1, ..., N by alpha_r=1/Nsum_(i=1)^Nz_i^r=(mu_r)/(sigma^r), (1) where z_i=(x_i-x^_)/(s_x). (2) The first few are alpha_1 = 0 (3) alpha_2 = 1 (4) ...

A multiplicative character is called unitary if it has absolute value 1 everywhere.

A solution zeta_k=e^(2piik/d) to the cyclotomic equation x^d=1. The de Moivre numbers give the coordinates in the complex plane of the polygon vertices of a regular polygon ...

The Pierce expansion, or alternated Egyptian product, of a real number 0<x<1 is the unique increasing sequence {a_1,a_2,...} of positive integers a_i such that ...

The Leibniz harmonic triangle is the number triangle given by 1/11/2 1/21/3 1/6 1/31/4 1/(12) 1/(12) 1/41/5 1/(20) 1/(30) 1/(20) 1/5 (1) (OEIS A003506), where each fraction ...

A tree (also called a bicentral tree) having two nodes that are graph centers. The numbers of bicentered trees on n=1, 2, ... nodes are 0, 1, 0, 1, 1, 3, 4, 11, 20, 51, 108 ...

For a polynomial P(x_1,x_2,...,x_k), the Mahler measure of P is defined by (1) Using Jensen's formula, it can be shown that for P(x)=aproduct_(i=1)^(n)(x-alpha_i), ...