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A function f(x) is said to be square integrable if int_(-infty)^infty|f(x)|^2dx is finite.

The function defined by y_+^alpha={y^alpha for y>0; 0 for y<=0. (1)

k_nu(x)=(e^(-x))/(Gamma(1+1/2nu))U(-1/2nu,0,2x) for x>0, where U is a confluent hypergeometric function of the second kind.

The Lommel polynomials R_(m,nu)(z) arise from the equation J_(m+nu)(z)=J_nu(z)R_(m,nu)(z)-J_(nu-1)(z)R_(m-1,nu+1)(z), (1) where J_nu(z) is a Bessel function of the first kind ...

The spherical Bessel function of the second kind, denoted y_nu(z) or n_nu(z), is defined by y_nu(z)=sqrt(pi/(2z))Y_(nu+1/2)(z), (1) where Y_nu(z) is a Bessel function of the ...

A discrete function A(n,k) is called closed form (or sometimes "hypergeometric") in two variables if the ratios A(n+1,k)/A(n,k) and A(n,k+1)/A(n,k) are both rational ...

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 ...

A function is said to be modular (or "elliptic modular") if it satisfies: 1. f is meromorphic in the upper half-plane H, 2. f(Atau)=f(tau) for every matrix A in the modular ...

delta(x-t)=sum_(n=0)^inftyphi_n(x)phi_n(t), where delta(x) is the delta function.

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