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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 ...

There are a couple of versions of this theorem. Basically, it says that any bounded linear functional T on the space of compactly supported continuous functions on X is the ...

The Rogers-Selberg identities are a set of three analytic q-series identities of Rogers-Ramanujan-type appearing as equation 33, 32, and 31 in Slater (1952), A(q) = ...

Affine functions represent vector-valued functions of the form f(x_1,...,x_n)=A_1x_1+...+A_nx_n+b. The coefficients can be scalars or dense or sparse matrices. The constant ...

The second-order ordinary differential equation y^('')+(y^')/x+(1-(nu^2)/(x^2))y=(x-nu)/(pix^2)sin(pinu) whose solutions are Anger functions.

The mathematical study of how given quantities can be approximated by other (usually simpler) ones under appropriate conditions. Approximation theory also studies the size ...

Let s(x,y,z) and t(x,y,z) be differentiable scalar functions defined at all points on a surface S. In computer graphics, the functions s and t often represent texture ...

The Brent-Salamin formula, also called the Gauss-Salamin formula or Salamin formula, is a formula that uses the arithmetic-geometric mean to compute pi. It has quadratic ...

Let p_n/q_n be the sequence of convergents of the continued fraction of a number alpha. Then a Brjuno number is an irrational number such that ...