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Half-angle formulas and formulas expressing trigonometric functions of an angle x/2 in terms of functions of an angle x. For real x, sin(1/2x) = ...

The half-normal distribution is a normal distribution with mean 0 and parameter theta limited to the domain x in [0,infty). It has probability and distribution functions ...

An elliptic function can be characterized by its real and imaginary half-periods omega_1 and omega_2 (Whittaker and Watson 1990, p. 428), sometimes also denoted ...

A root-finding algorithm also known as the tangent hyperbolas method or Halley's rational formula. As in Halley's irrational formula, take the second-order Taylor series ...

An apodization function chosen to minimize the height of the highest sidelobe (Hamming and Tukey 1949, Blackman and Tukey 1959). The Hamming function is given by ...

A surface given by the parametric equations x(u,v) = u (1) y(u,v) = v (2) z(u,v) = 1/3u^3+uv^2+2(u^2-v^2). (3) The handkerchief surface has stationary points summarized in ...

A handle is a topological structure which can be thought of as the object produced by puncturing a surface twice, attaching a zip around each puncture travelling in opposite ...

It is always possible to write a sum of sinusoidal functions f(theta)=acostheta+bsintheta (1) as a single sinusoid the form f(theta)=ccos(theta+delta). (2) This can be done ...

To solve the heat conduction equation on a two-dimensional disk of radius a=1, try to separate the equation using U(r,theta,t)=R(r)Theta(theta)T(t). (1) Writing the theta and ...

A family of operators mapping each space M_k of modular forms onto itself. For a fixed integer k and any positive integer n, the Hecke operator T_n is defined on the set M_k ...