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The Euler polynomial E_n(x) is given by the Appell sequence with g(t)=1/2(e^t+1), (1) giving the generating function (2e^(xt))/(e^t+1)=sum_(n=0)^inftyE_n(x)(t^n)/(n!). (2) ...

The continued fraction of A is [1; 3, 1, 1, 5, 1, 1, 1, 3, 12, 4, 1, 271, 1, ...] (OEIS A087501). A plot of the first 256 terms of the continued fraction represented as a ...

The Gram series is an approximation to the prime counting function given by G(x)=1+sum_(k=1)^infty((lnx)^k)/(kk!zeta(k+1)), (1) where zeta(z) is the Riemann zeta function ...

The Gregory series is a pi formula found by Gregory and Leibniz and obtained by plugging x=1 into the Leibniz series, pi/4=sum_(k=1)^infty((-1)^(k+1))/(2k-1)=1-1/3+1/5-... ...

A hexagon tiling is a tiling of the plane by identical hexagons. The regular hexagon forms a regular tessellation, also called a hexagonal grid, illustrated above. There are ...

A theorem, also known as Bachet's conjecture, which Bachet inferred from a lack of a necessary condition being stated by Diophantus. It states that every positive integer can ...

Let s=1/(sqrt(2pi))[Gamma(1/4)]^2=5.2441151086... (1) (OEIS A064853) be the arc length of a lemniscate with a=1. Then the lemniscate constant is the quantity L = 1/2s (2) = ...

A maximal clique is a clique that cannot be extended by including one more adjacent vertex, meaning it is not a subset of a larger clique. A maximum clique (i.e., clique of ...

Let Sigma(n)=sum_(i=1)^np_i (1) be the sum of the first n primes (i.e., the sum analog of the primorial function). The first few terms are 2, 5, 10, 17, 28, 41, 58, 77, ... ...

A sequence of n-tuples that fills n-space more uniformly than uncorrelated random points, sometimes also called a low-discrepancy sequence. Although the ordinary uniform ...