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The series sum_(k=1)^inftykr^k=sum_(k=1)^inftysum_(i=k)^inftyr^i=r/((1-r)^2), valid for 0<r<1.

The first Göllnitz-Gordon identity states that the number of partitions of n in which the minimal difference between parts is at least 2, and at least 4 between even parts, ...

A sampling phenomenon produced when a waveform is not sampled uniformly at an interval t each time, but rather at a series of slightly shifted intervals t+Deltat_i such that ...

The Lerch transcendent is generalization of the Hurwitz zeta function and polylogarithm function. Many sums of reciprocal powers can be expressed in terms of it. It is ...

An operator L^~ is said to be linear if, for every pair of functions f and g and scalar t, L^~(f+g)=L^~f+L^~g and L^~(tf)=tL^~f.

Moving medians are implemented in the Wolfram Language as MovingMedian[data, n].

The value for zeta(2)=sum_(k=1)^infty1/(k^2) (1) can be found using a number of different techniques (Apostol 1983, Choe 1987, Giesy 1972, Holme 1970, Kimble 1987, Knopp and ...

For |q|<1, the Rogers-Ramanujan identities are given by (Hardy 1999, pp. 13 and 90), sum_(n=0)^(infty)(q^(n^2))/((q)_n) = 1/(product_(n=1)^(infty)(1-q^(5n-4))(1-q^(5n-1))) ...

The modular equation of degree five can be written (u/v)^3+(v/u)^3=2(u^2v^2-1/(u^2v^2)).

A method for finding recurrence relations for hypergeometric polynomials directly from the series expansions of the polynomials. The method is effective and easily ...