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The modular equation of degree n gives an algebraic connection of the form (K^'(l))/(K(l))=n(K^'(k))/(K(k)) (1) between the transcendental complete elliptic integrals of the ...

A function is said to be modular (or "elliptic modular") if it satisfies: 1. f is meromorphic in the upper half-plane H, 2. f(Atau)=f(tau) for every matrix A in the modular ...

A New Kind of Science is a seminal work on simple programs by Stephen Wolfram. In 1980, Wolfram's studies found unexpected behavior in a collection of simple computer ...

Informally, a function f is a one-way function if 1. The description of f is publicly known and does not require any secret information for its operation. 2. Given x, it is ...

One of the symbols ( or ) used to denote grouping. Parentheses have a great many specialized meanings in mathematics. A few of these are described below. 1. Parentheses are ...

Define a pebbling move as a transer of two pebbles from one vertex of a graph edge to an adjacent vertex with one of the pebbles being removed in transit as a toll. The ...

product_(k=1)^(infty)(1-x^k) = sum_(k=-infty)^(infty)(-1)^kx^(k(3k+1)/2) (1) = 1+sum_(k=1)^(infty)(-1)^k[x^(k(3k-1)/2)+x^(k(3k+1)/2)] (2) = (x)_infty (3) = ...

Porter's constant is the constant appearing in formulas for the efficiency of the Euclidean algorithm, C = (6ln2)/(pi^2)[3ln2+4gamma-(24)/(pi^2)zeta^'(2)-2]-1/2 (1) = ...

A prime ideal is an ideal I such that if ab in I, then either a in I or b in I. For example, in the integers, the ideal a=<p> (i.e., the multiples of p) is prime whenever p ...

As first shown by Meyer and Ritchie (1967), do-loops (which have a fixed iteration limit) are a special case of while-loops. A function that can be implemented using only ...