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If a complex function is analytic at all finite points of the complex plane C, then it is said to be entire, sometimes also called "integral" (Knopp 1996, p. 112). Any ...

A function is a relation that uniquely associates members of one set with members of another set. More formally, a function from A to B is an object f such that every a in A ...

A modular form which is not allowed to have poles in the upper half-plane H or at iinfty.

The infimum of all number a for which |f(z)|<=exp(|z|^a) holds for all |z|>r and f an entire function, is called the order of f, denoted lambda=lambda(f) (Krantz 1999, p. ...

An entire function which is a generalization of the Bessel function of the first kind defined by J_nu(z)=1/piint_0^picos(nutheta-zsintheta)dtheta. Anger's original function ...

The entire function phi(rho,beta;z)=sum_(k=0)^infty(z^k)/(k!Gamma(rhok+beta)), where rho>-1 and beta in C, named after the British mathematician E. M. Wright.

A complex function is said to be analytic on a region R if it is complex differentiable at every point in R. The terms holomorphic function, differentiable function, and ...

A meromorphic function is a single-valued function that is analytic in all but possibly a discrete subset of its domain, and at those singularities it must go to infinity ...

For any alpha in A (where A denotes the set of algebraic numbers), let |alpha|^_ denote the maximum of moduli of all conjugates of alpha. Then a function ...

The most general form of "an" exponential function is a power-law function of the form f(x)=ab^(cx+d), (1) where a, c, and d are real numbers, b is a positive real number, ...