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Ore (1962) noted that not only does a tree possesses a unique shortest path between any two vertices, but that there also exist also other connected graphs having the same ...

Kloosterman's sum is defined by S(u,v,n)=sum_(h)exp[(2pii(uh+vh^_))/n], (1) where h runs through a complete set of residues relatively prime to n and h^_ is defined by hh^_=1 ...

Let L_n be the n×n matrix whose (i,j)th entry is 1 if j divides i and 0 otherwise, let Phi_n be the n×n diagonal matrix diag(phi(1),phi(2),...,phi(n)), where phi(n) is the ...

A sufficient condition on the Lindeberg-Feller central limit theorem. Given random variates X_1, X_2, ..., let <X_i>=0, the variance sigma_i^2 of X_i be finite, and variance ...

The median of a statistical distribution with distribution function D(x) is the value x such D(x)=1/2. For a symmetric distribution, it is therefore equal to the mean. Given ...

The stevedore's knot is the 6-crossing prime knot 6_1. It is implemented in the Wolfram Language as KnotData["Stevedore"]. It has braid word ...

A generalized continued fraction is an expression of the form b_0+(a_1)/(b_1+(a_2)/(b_2+(a_3)/(b_3+...))), (1) where the partial numerators a_1,a_2,... and partial ...

The Walsh functions consist of trains of square pulses (with the allowed states being -1 and 1) such that transitions may only occur at fixed intervals of a unit time step, ...

The modern definition of the q-hypergeometric function is _rphi_s[alpha_1,alpha_2,...,alpha_r; beta_1,...,beta_s;q,z] ...

The inverse of the Laplace transform, given by F(t)=1/(2pii)int_(gamma-iinfty)^(gamma+iinfty)e^(st)f(s)ds, where gamma is a vertical contour in the complex plane chosen so ...