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The function defined by chi_nu(z)=sum_(k=0)^infty(z^(2k+1))/((2k+1)^nu). (1) It is related to the polylogarithm by chi_nu(z) = 1/2[Li_nu(z)-Li_nu(-z)] (2) = ...

If a function phi is harmonic in a sphere, then the value of phi at the center of the sphere is the arithmetic mean of its value on the surface.

The fraction of odd values of the partition function P(n) is roughly 50%, independent of n, whereas odd values of Q(n) occur with ever decreasing frequency as n becomes ...

A multiplicative number theoretic function is a number theoretic function f that has the property f(mn)=f(m)f(n) (1) for all pairs of relatively prime positive integers m and ...

It is thought that the totient valence function N_phi(m)>=2, i.e., if there is an n such that phi(n)=m, then there are at least two solutions n. This assertion is called ...

N_phi(m) is the number of integers n for which the totient function phi(n)=m, also called the multiplicity of m (Guy 1994). Erdős (1958) proved that if a multiplicity occurs ...

Minkowski's question mark function is the function y=?(x) defined by Minkowski for the purpose of mapping the quadratic surds in the open interval (0,1) into the rational ...

The modified Lommel functions of the first and second kind give the solution to the Lommel differential equation with a minus sign in front of the linear term, i.e., ...

The inhomogeneous Helmholtz differential equation is del ^2psi(r)+k^2psi(r)=rho(r), (1) where the Helmholtz operator is defined as L^~=del ^2+k^2. The Green's function is ...

The parabolic cylinder functions are a class of functions sometimes called Weber functions. There are a number of slightly different definitions in use by various authors. ...