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The hacoversine, also known as the hacoversed sine and cohaversine, is a little-used trigonometric function defined by hacoversin(z) = coversinz (1) = 1/2(1-sinz), (2) where ...

The Lorentzian function is the singly peaked function given by L(x)=1/pi(1/2Gamma)/((x-x_0)^2+(1/2Gamma)^2), (1) where x_0 is the center and Gamma is a parameter specifying ...

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 inverse function of the logarithm, defined such that log_b(antilog_bz)=z=antilog_b(log_bz). The antilogarithm in base b of z is therefore b^z.

A synonym for analytic function, regular function, differentiable function, complex differentiable function, and holomorphic map (Krantz 1999, p. 16). The word derives from ...

The hyperbolic sine integral, often called the "Shi function" for short, is defined by Shi(z)=int_0^z(sinht)/tdt. (1) The function is implemented in the Wolfram Language as ...

A map is a way of associating unique objects to every element in a given set. So a map f:A|->B from A to B is a function f such that for every a in A, there is a unique ...

Let p run over all distinct primitive ordered periodic geodesics, and let tau(p) denote the positive length of p, then the Selberg zeta function is defined as ...

There are a number of functions in various branches of mathematics known as Riemann functions. Examples include the Riemann P-series, Riemann-Siegel functions, Riemann theta ...

Let D=D(z_0,R) be an open disk, and let u be a harmonic function on D such that u(z)>=0 for all z in D. Then for all z in D, we have 0<=u(z)<=(R/(R-|z-z_0|))^2u(z_0).