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Lehmer (1938) showed that every positive irrational number x has a unique infinite continued cotangent representation of the form x=cot[sum_(k=0)^infty(-1)^kcot^(-1)b_k], (1) ...

The Lehmer cotangent expansion for which the convergence is slowest occurs when the inequality in the recurrence equation b_k>=b_(k-1)^2+b_(k-1)+1. (1) for ...

The conjecture that, for any triangle, 8omega^3<ABC (1) where A, B, and C are the vertex angles of the triangle and omega is the Brocard angle. The Abi-Khuzam inequality ...

The term "characteristic" has many different uses in mathematics. In general, it refers to some property that inherently describes a given mathematical object, for example ...

The inverse tangent is the multivalued function tan^(-1)z (Zwillinger 1995, p. 465), also denoted arctanz (Abramowitz and Stegun 1972, p. 79; Harris and Stocker 1998, p. 311; ...

An equation involving a function f(x) and integrals of that function to solved for f(x). If the limits of the integral are fixed, an integral equation is called a Fredholm ...

The partial differential equation u_t+u_(xxxxx)+30uu_(xxx)+30u_xu_(xx)+180u^2u_x=0.

A differential equation is an equation that involves the derivatives of a function as well as the function itself. If partial derivatives are involved, the equation is called ...

An equation of the form f(x,y,...)=0, where f contains a finite number of independent variables, known functions, and unknown functions which are to be solved for. Many ...

For the hyperbolic partial differential equation u_(xy) = F(x,y,u,p,q) (1) p = u_x (2) q = u_y (3) on a domain Omega, Goursat's problem asks to find a solution u(x,y) of (3) ...