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A Gaussian integer is a complex number a+bi where a and b are integers. The Gaussian integers are members of the imaginary quadratic field Q(sqrt(-1)) and form a ring often ...

A lattice reduction algorithm, named after discoverers Lenstra, Lenstra, and Lovasz (1982), that produces a lattice basis of "short" vectors. It was noticed by Lenstra et al. ...

A function f is said to be an entire modular form of weight k if it satisfies 1. f is analytic in the upper half-plane H, 2. f((atau+b)/(ctau+d))=(ctau+d)^kf(tau) whenever [a ...

Approximants derived by expanding a function as a ratio of two power series and determining both the numerator and denominator coefficients. Padé approximations are usually ...

Plouffe's constants are numbers arising in summations of series related to r_n=f(2^n) where f is a trigonometric function. Define the Iverson bracket function rho(x)={1 for ...

The Rhind papyrus is a famous document from the Egyptian Middle Kingdom that dates to 1650 BC. It was purchased by Henry Rhind in Egypt in 1858, and placed in the British ...

A rose curve, also called Grandi's rose or the multifolium, is a curve which has the shape of a petalled flower. This curve was named rhodonea by the Italian mathematician ...

The Somos sequences are a set of related symmetrical recurrence relations which, surprisingly, always give integers. The Somos sequence of order k, or Somos-k sequence, is ...

A symmetric bilinear form on a vector space V is a bilinear function Q:V×V->R (1) which satisfies Q(v,w)=Q(w,v). For example, if A is a n×n symmetric matrix, then ...

A pair of closed form functions (F,G) is said to be a Wilf-Zeilberger pair if F(n+1,k)-F(n,k)=G(n,k+1)-G(n,k). (1) The Wilf-Zeilberger formalism provides succinct proofs of ...