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The function f_theta(z)=z/((1+e^(itheta)z)^2) (1) defined on the unit disk |z|<1. For theta in [0,2pi), the Köbe function is a schlicht function f(z)=z+sum_(j=2)^inftya_jz^j ...

The Griewank function is a function widely used to test the convergence of optimization functions. The Griewank function of order n is defined by ...

A function which satisfies f(tx,ty)=t^nf(x,y) for a fixed n. Means, the Weierstrass elliptic function, and triangle center functions are homogeneous functions. A ...

A function which is not defined explicitly, but rather is defined in terms of an algebraic relationship (which can not, in general, be "solved" for the function in question). ...

The Cantor function F(x) is the continuous but not absolutely continuous function on [0,1] which may be defined as follows. First, express x in ternary. If the resulting ...

The delta function is a generalized function that can be defined as the limit of a class of delta sequences. The delta function is sometimes called "Dirac's delta function" ...

The score function u(theta) is the partial derivativeof the log-likelihood function F(theta)=lnL(theta), where L(theta) is the standard likelihood function. Defining the ...

A composition of a function f degreesf with itself gives a nested function f(f(x)), f degreesf degreesf which gives f(f(f(x)), etc. Function nesting is implemented in the ...

Thomae's theorem, also called Thomae's transformation, is the generalized hypergeometric function identity (1) where Gamma(z) is the gamma function, _3F_2(a,b,c;e,f;z) is a ...

The Mangoldt function is the function defined by Lambda(n)={lnp if n=p^k for p a prime; 0 otherwise, (1) sometimes also called the lambda function. exp(Lambda(n)) has the ...