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The wave equation in prolate spheroidal coordinates is del ...

The Rogers-Selberg identities are a set of three analytic q-series identities of Rogers-Ramanujan-type appearing as equation 33, 32, and 31 in Slater (1952), A(q) = ...

The ruliad may be defined as the entangled limit of everything that is computationally possible, i.e., the result of following all possible computational rules in all ...

The Dedekind eta function is defined over the upper half-plane H={tau:I[tau]>0} by eta(tau) = q^_^(1/24)(q^_)_infty (1) = q^_^(1/24)product_(k=1)^(infty)(1-q^_^k) (2) = ...

A double sum is a series having terms depending on two indices, sum_(i,j)b_(ij). (1) A finite double series can be written as a product of series ...

An Eisenstein series with half-period ratio tau and index r is defined by G_r(tau)=sum^'_(m=-infty)^inftysum^'_(n=-infty)^infty1/((m+ntau)^r), (1) where the sum sum^(') ...

erf(z) is the "error function" encountered in integrating the normal distribution (which is a normalized form of the Gaussian function). It is an entire function defined by ...

The floor function |_x_|, also called the greatest integer function or integer value (Spanier and Oldham 1987), gives the largest integer less than or equal to x. The name ...

A generating function f(x) is a formal power series f(x)=sum_(n=0)^inftya_nx^n (1) whose coefficients give the sequence {a_0,a_1,...}. The Wolfram Language command ...

The series sum_(k=1)^infty1/k (1) is called the harmonic series. It can be shown to diverge using the integral test by comparison with the function 1/x. The divergence, ...