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A function which has infinitely many derivatives at a point. If a function is not polygenic, it is monogenic.

Stirling's approximation gives an approximate value for the factorial function n! or the gamma function Gamma(n) for n>>1. The approximation can most simply be derived for n ...

Define S_n(x) = sum_(k=1)^(infty)(sin(kx))/(k^n) (1) C_n(x) = sum_(k=1)^(infty)(cos(kx))/(k^n), (2) then the Clausen functions are defined by ...

A generalized Fourier series is a series expansion of a function based on the special properties of a complete orthogonal system of functions. The prototypical example of ...

A generalization of the Lebesgue integral. A measurable function f(x) is called A-integrable over the closed interval [a,b] if m{x:|f(x)|>n}=O(n^(-1)), (1) where m is the ...

A solution to a problem that can be written in "closed form" in terms of known functions, constants, etc., is often called an analytic solution. Note that this use of the ...

The nth order Bernstein expansion of a function f(x) in terms of a variable x is given by B_n(f,x)=sum_(j=0)^n(n; j)x^j(1-x)^(n-j)f(j/n), (1) (Gzyl and Palacios 1997, Mathé ...

A G-space provides local notions of harmonic, hyperharmonic, and superharmonic functions. When there exists a nonconstant superharmonic function greater than 0, it is a ...

Define the zeta function of a variety over a number field by taking the product over all prime ideals of the zeta functions of this variety reduced modulo the primes. Hasse ...

If there are two functions F_1(t) and F_2(t) with the same integral transform T[F_1(t)]=T[F_2(t)]=f(s), (1) then a null function can be defined by delta_0(t)=F_1(t)-F_2(t) ...