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Apéry's numbers are defined by A_n = sum_(k=0)^(n)(n; k)^2(n+k; k)^2 (1) = sum_(k=0)^(n)([(n+k)!]^2)/((k!)^4[(n-k)!]^2) (2) = _4F_3(-n,-n,n+1,n+1;1,1,1;1), (3) where (n; k) ...

The v coordinates are the asymptotic angle of confocal hyperbolic cylinders symmetrical about the x-axis. The u coordinates are confocal elliptic cylinders centered on the ...

The pedal curve of an epicycloid x = (a+b)cost-b[((a+b)t)/b] (1) y = (a+b)sint-bsin[((a+b)t)/b] (2) with pedal point at the origin is x_p = 1/2(a+2b){cost-cos[((a+b)t)/b]} ...

A curve also known as Gutschoven's curve which was first studied by G. van Gutschoven around 1662 (MacTutor Archive). It was also studied by Newton and, some years later, by ...

The links curve is the quartic curve given by the Cartesian equation (x^2+y^2-3x)^2=4x^2(2-x). (1) The area enclosed by the outer envelope is A_(envelope)=1/6(9pi+8) (2) and ...

Let alpha, -beta, and -gamma^(-1) be the roots of the cubic equation t^3+2t^2-t-1=0, (1) then the Rogers L-function satisfies L(alpha)-L(alpha^2) = 1/7 (2) ...

Clean tile is a game investigated by Buffon (1777) in which players bet on the number of different tiles a thrown coin will partially cover on a floor that is regularly ...

A transcendental number is a (possibly complex) number that is not the root of any integer polynomial, meaning that it is not an algebraic number of any degree. Every real ...

The word multiplicity is a general term meaning "the number of values for which a given condition holds." For example, the term is used to refer to the value of the totient ...

In most computer programs and computing environments, the precision of any calculation (even including addition) is limited by the word size of the computer, that is, by ...