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The second-order ordinary differential equation xy^('')+(c-x)y^'-ay=0, sometimes also called Kummer's differential equation (Slater 1960, p. 2; Zwillinger 1997, p. 124). It ...

A place nu of a number field k is an isomorphism class of field maps k onto a dense subfield of a nondiscrete locally compact field k_nu. In the function field case, let F be ...

An integrating factor is a function by which an ordinary differential equation can be multiplied in order to make it integrable. For example, a linear first-order ordinary ...

The Lie derivative of tensor T_(ab) with respect to the vector field X is defined by L_XT_(ab)=lim_(deltax->0)(T_(ab)^'(x^')-T_(ab)(x))/(deltax). (1) Explicitly, it is given ...

Serre's problem, also called Serre's conjecture, asserts that the implication "free module ==> projective module" can be reversed for every module over the polynomial ring ...

An algorithm for computing an Egyptian fraction, called the Farey sequence method by Bleicher (1972).

A rational number expressed in the form a/b (in-line notation) or a/b (traditional "display" notation), where a is called the numerator and b is called the denominator. When ...

Given a Farey sequence with consecutive terms h/k and h^'/k^', then the mediant is defined as the reduced form of the fraction (h+h^')/(k+k^').

A method for computing an Egyptian fraction. This method always terminates (Beeckmans 1993).

Lagrange's continued fraction theorem, proved by Lagrange in 1770, states that any positive quadratic surd sqrt(a) has a regular continued fraction which is periodic after ...