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The odd divisor function sigma_k^((o))(n)=sum_(d|n; d odd)d^k (1) is the sum of kth powers of the odd divisors of a number n. It is the analog of the divisor function for odd ...

An elliptic function with no poles in a fundamental cell is a constant.

The two-argument Ramanujan function is defined by phi(a,n) = 1+2sum_(k=1)^(n)1/((ak)^3-ak) (1) = 1-1/a(H_(-1/a)+H_(1/a)+2H_n-H_(n-1/a)-H_(n+1/a)). (2) The one-argument ...

The convex hull of two or more functions is the largest function that is concave from above and does not exceed the given functions.

Given a function f(x)=f_0(x), write f_1=f^'(x) and define the Sturm functions by f_n(x)=-{f_(n-2)(x)-f_(n-1)(x)[(f_(n-2)(x))/(f_(n-1)(x))]}, (1) where [P(x)/Q(x)] is a ...

A "curve" (i.e., a continuous map of a one-dimensional interval) into a two-dimensional area (a plane-filling function) or a three-dimensional volume.

An anti-analytic function is a function f satisfying the condition (df)/(dz)=0. (1) Using the result ...

An asymmetrical apodization function defined by M(x,b,d)={0 for x<-b; (x-b)/(2b) for -b<x<b; 1 for b<x<b+2d; 0 for x<b+2d, (1) where the two-sided portion is 2b long (total) ...

The Coulomb wave function is a special case of the confluent hypergeometric function of the first kind. It gives the solution to the radial Schrödinger equation in the ...

Let Pi(x) be the rectangle function, then the Fourier transform is F_x[Pi(x)](k)=sinc(pik), where sinc(x) is the sinc function.