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An asymptotic series is a series expansion of a function in a variable x which may converge or diverge (Erdélyi 1987, p. 1), but whose partial sums can be made an arbitrarily ...

The complete elliptic integral of the first kind K(k), illustrated above as a function of the elliptic modulus k, is defined by K(k) = F(1/2pi,k) (1) = ...

The hypersine (n-dimensional sine function) is a function of a vertex angle of an n-dimensional parallelotope or simplex. If the content of the parallelotope is P and the ...

Brocard's conjecture states that pi(p_(n+1)^2)-pi(p_n^2)>=4 for n>=2, where pi(n) is the prime counting function and p_n is the nth prime. For n=1, 2, ..., the first few ...

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 ...

Let G be a Lie group and let rho be a group representation of G on C^n (for some natural number n), which is continuous in the sense that the function G×C^n->C^n defined by ...

A generalization of Fermat's little theorem. Euler published a proof of the following more general theorem in 1736. Let phi(n) denote the totient function. Then a^(phi(n))=1 ...

An elliptic fixed point of a differential equation is a fixed point for which the stability matrix has purely imaginary eigenvalues lambda_+/-=+/-iomega (for omega>0). An ...

A complex manifold for which the exterior derivative of the fundamental form Omega associated with the given Hermitian metric vanishes, so dOmega=0. In other words, it is a ...

A wavelet used in multiresolution representation to analyze the information content of images. The wavelet is defined by ...