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The Champernowne constant has decimal expansion C=0.1234567891011... (OEIS A033307). The Earls sequence (starting position of n copies of the digit n) for e is given for n=1, ...

A two-dimensional map similar to the Hénon map but with the term -alphax_n^2 replaced by -alpha|x_n|. It is given by the equations x_(n+1) = 1-alpha|x_n|+y_n (1) y_(n+1) = ...

A proper factor of a positive integer n is a factor of n other than 1 or n (Derbyshire 2004, p. 32). For example, 2 and 3 are positive proper factors of 6, but 1 and 6 are ...

Clausen's _4F_3 identity _4F_3(a,b,c,d; e,f,g;1)=((2a)_(|d|)(a+b)_(|d|)(2b)_(|d|))/((2a+2b)_(|d|)a_(|d|)b_(|d|)), (1) holds for a+b+c-d=1/2, e=a+b+1/2, a+f=d+1=b+g, where d a ...

A circle bundle pi:E->M is a fiber bundle whose fibers pi^(-1)(x) are circles. It may also have the structure of a principal bundle if there is an action of SO(2) that ...

The complementary Bell numbers, also called the Uppuluri-Carpenter numbers, B^~_n=sum_(k=0)^n(-1)^kS(n,k) (1) where S(n,k) is a Stirling number of the second kind, are ...

Odd values of Q(n) are 1, 1, 3, 5, 27, 89, 165, 585, ... (OEIS A051044), and occur with ever decreasing frequency as n becomes large (unlike P(n), for which the fraction of ...

An alternating permutation is an arrangement of the elements c_1, ..., c_n such that no element c_i has a magnitude between c_(i-1) and c_(i+1) is called an alternating (or ...

The orthogonal polynomials defined by h_n^((alpha,beta))(x,N)=((-1)^n(N-x-n)_n(beta+x+1)_n)/(n!) ×_3F_2(-n,-x,alpha+N-x; N-x-n,-beta-x-n;1) =((-1)^n(N-n)_n(beta+1)_n)/(n!) ...

The inverse erf function is the inverse function erfc^(-1)(z) of erfc(x) such that erfc(erfc^(-1)(x))=erfc^(-1)(erfc(x)), (1) with the first identity holding for 0<x<2 and ...