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The series z=ln(e^xe^y) (1) for noncommuting variables x and y. The first few terms are z_1 = x+y (2) z_2 = 1/2(xy-yx) (3) z_3 = 1/(12)(x^2y+xy^2-2xyx+y^2x+yx^2-2yxy) (4) z_4 ...

Let E_n(f) be the error of the best uniform approximation to a real function f(x) on the interval [-1,1] by real polynomials of degree at most n. If alpha(x)=|x|, (1) then ...

The Carlson elliptic integrals, also known as the Carlson symmetric forms, are a standard set of canonical elliptic integrals which provide a convenient alternative to ...

A method of computing the determinant of a square matrix due to Charles Dodgson (1866) (who is more famous under his pseudonym Lewis Carroll). The method is useful for hand ...

Given an expression involving known constants, integration in finite terms, computation of limits, etc., the constant problem is the determination of if the expression is ...

The number d(n) of monotone Boolean functions of n variables (equivalent to one more than the number of antichains on the n-set {1,2,...,n}) is called the nth Dedkind number. ...

The quantum electrodynamical law which applies to spin-1/2 particles and is the relativistic generalization of the Schrödinger equation. In 3+1 dimensions (three space ...

The first practical algorithm for determining if there exist integers a_i for given real numbers x_i such that a_1x_1+a_2x_2+...+a_nx_n=0, or else establish bounds within ...

According to Hardy and Wright (1979), the 44-digit Ferrier's prime determined to be prime using only a mechanical calculator, is the largest prime found before the days of ...

In the IEEE 754-2008 standard (referred to as IEEE 754 henceforth), a floating-point representation is an unencoded member of a floating-point format which represents either ...