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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-... ...

Define the sequence a_0=1, a_1=x, and a_n=(a_(n-2))/(1+a_(n-1)) (1) for n>=0. The first few values are a_2 = 1/(1+x) (2) a_3 = (x(1+x))/(2+x) (3) a_4 = ...

The base 16 notational system for representing real numbers. The digits used to represent numbers using hexadecimal notation are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, ...

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 ...

The hyperbolic cotangent is defined as cothz=(e^z+e^(-z))/(e^z-e^(-z))=(e^(2z)+1)/(e^(2z)-1). (1) The notation cthz is sometimes also used (Gradshteyn and Ryzhik 2000, p. ...

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 ...

The base 8 notational system for representing real numbers. The digits used are 0, 1, 2, 3, 4, 5, 6, and 7, so that 8_(10) (8 in base 10) is represented as 10_8 ...