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A two-regular graph is a regular graph for which all local degrees are 2. A two-regular graph consists of one or more (disconnected) cycles. The numbers a_n of two-regular ...

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 ...

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 ...

The wallpaper groups are the 17 possible plane symmetry groups. They are commonly represented using Hermann-Mauguin-like symbols or in orbifold notation (Zwillinger 1995, p. ...

The constant e is base of the natural logarithm. e is sometimes known as Napier's constant, although its symbol (e) honors Euler. e is the unique number with the property ...

There are several related series that are known as the binomial series. The most general is (x+a)^nu=sum_(k=0)^infty(nu; k)x^ka^(nu-k), (1) where (nu; k) is a binomial ...

The Laguerre differential equation is given by xy^('')+(1-x)y^'+lambday=0. (1) Equation (1) is a special case of the more general associated Laguerre differential equation, ...

The lemniscate functions arise in rectifying the arc length of the lemniscate. The lemniscate functions were first studied by Jakob Bernoulli and Giulio Fagnano. A historical ...

Consider a line segment of length 1, and pick a point x at random between [0,1]. This point x divides the line into line segments of length x and 1-x. If a set of points are ...

The negative binomial distribution, also known as the Pascal distribution or Pólya distribution, gives the probability of r-1 successes and x failures in x+r-1 trials, and ...