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Fermat's spiral, also known as the parabolic spiral, is an Archimedean spiral with m=2 having polar equation r^2=a^2theta. (1) This curve was discussed by Fermat in 1636 ...

There are (at least) two mathematical objects known as Weierstrass forms. The first is a general form into which an elliptic curve over any field K can be transformed, given ...

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). ...

The q-analog of integration is given by int_0^1f(x)d(q,x)=(1-q)sum_(i=0)^inftyf(q^i)q^i, (1) which reduces to int_0^1f(x)dx (2) in the case q->1^- (Andrews 1986 p. 10). ...

A statistical distribution published by William Gosset in 1908. His employer, Guinness Breweries, required him to publish under a pseudonym, so he chose "Student." Given N ...

A system of equation types obtained by generalizing the differential equation for the normal distribution (dy)/(dx)=(y(m-x))/a, (1) which has solution y=Ce^((2m-x)x/(2a)), ...

alpha is called a predecessor if there is no ordinal number beta such that beta+1=alpha.

If (sinalpha)/(sinbeta)=m/n, then (tan[1/2(alpha-beta)])/(tan[1/2(alpha+beta)])=(m-n)/(m+n).

If there is a (nu,nu^') correspondence between two curves of curve genus p and p^' and the number of branch points properly counted are beta and beta^', then ...

The continuous distribution with parameters m and b>0 having probability and distribution functions P(x) = (e^(-(x-m)/b))/(b[1+e^(-(x-m)/b)]^2) (1) D(x) = 1/(1+e^(-(x-m)/b)) ...