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The h-statistic h_r is the unique symmetric unbiased estimator for a central moment of a distribution <h_r>=mu_r. (1) In addition, the variance var(h_r)=<(h_r-mu_r)^2> (2) is ...

The q-analog of pi pi_q can be defined by setting a=0 in the q-factorial [a]_q!=1(1+q)(1+q+q^2)...(1+q+...+q^(a-1)) (1) to obtain ...

Define the nome by q=e^(-piK^'(k)/K(k))=e^(ipitau), (1) where K(k) is the complete elliptic integral of the first kind with modulus k, K^'(k)=K(sqrt(1-k^2)) is the ...

A circle is the set of points in a plane that are equidistant from a given point O. The distance r from the center is called the radius, and the point O is called the center. ...

Scan the decimal expansion of a constant (including any digits to the left of the decimal point) until all n-digit strings have been seen (including 0-padded strings). The ...

A cubic symmetric graph is a symmetric cubic (i.e., regular of order 3). Such graphs were first studied by Foster (1932). They have since been the subject of much interest ...

A Diophantine equation is an equation in which only integer solutions are allowed. Hilbert's 10th problem asked if an algorithm existed for determining whether an arbitrary ...

The regular polygon of 17 sides is called the heptadecagon, or sometimes the heptakaidecagon. Gauss proved in 1796 (when he was 19 years old) that the heptadecagon is ...

Pascal's triangle is a number triangle with numbers arranged in staggered rows such that a_(nr)=(n!)/(r!(n-r)!)=(n; r), (1) where (n; r) is a binomial coefficient. The ...

In its original form, the Poincaré conjecture states that every simply connected closed three-manifold is homeomorphic to the three-sphere (in a topologist's sense) S^3, ...