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Define the nome by q=e^(-piK^'(k)/K(k))=e^(ipitau), (1) where K(k) is the complete elliptic integral of the first kind with modulus k, K^'(k)=K(sqrt(1-k^2)) is the ...

Dawson's integral (Abramowitz and Stegun 1972, pp. 295 and 319), also sometimes called Dawson's function, is the entire function given by the integral F(x) = ...

Given a Poisson process, the probability of obtaining exactly n successes in N trials is given by the limit of a binomial distribution P_p(n|N)=(N!)/(n!(N-n)!)p^n(1-p)^(N-n). ...

Two sets A and B are said to be independent if their intersection A intersection B=emptyset, where emptyset is the empty set. For example, {A,B,C} and {D,E} are independent, ...

A matrix whose elements may contain complex numbers. The matrix product of two 2×2 complex matrices is given by (1) where R_(11) = ...

In general, an integer n is divisible by d iff the digit sum s_(d+1)(n) is divisible by d. Write a positive decimal integer a out digit by digit in the form ...

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^(') ...

A finite field is a field with a finite field order (i.e., number of elements), also called a Galois field. The order of a finite field is always a prime or a power of a ...

A curve also known as the Gerono lemniscate. It is given by Cartesian coordinates x^4=a^2(x^2-y^2), (1) polar coordinates, r^2=a^2sec^4thetacos(2theta), (2) and parametric ...

The Menger sponge is a fractal which is the three-dimensional analog of the Sierpiński carpet. The nth iteration of the Menger sponge is implemented in the Wolfram Language ...