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The angles mpi/n (with m,n integers) for which the trigonometric functions may be expressed in terms of finite root extraction of real numbers are limited to values of m ...

The modern definition of the q-hypergeometric function is _rphi_s[alpha_1,alpha_2,...,alpha_r; beta_1,...,beta_s;q,z] ...

Given a series of positive terms u_i and a sequence of positive constants {a_i}, use Kummer's test rho^'=lim_(n->infty)(a_n(u_n)/(u_(n+1))-a_(n+1)) (1) with a_n=n, giving ...

A cylindrical wedge, also called a cylindrical hoof or cylindrical ungula, is a wedge cut from a cylinder by slicing with a plane that intersects the base of the cylinder. ...

Given an infinitive sequence {x_n} with associative array a(i,j), then {x_n} is said to be a fractal sequence 1. If i+1=x_n, then there exists m<n such that i=x_m, 2. If h<i, ...

For R[n]>-1 and R[z]>0, Pi(z,n) = n^zint_0^1(1-x)^nx^(z-1)dx (1) = (n!)/((z)_(n+1))n^z (2) = B(z,n+1), (3) where (z)_n is the Pochhammer symbol and B(p,q) is the beta ...

Whipple derived a great many identities for generalized hypergeometric functions, many of which are consequently known as Whipple's identities (transformations, etc.). Among ...

The point group C_1 is a group on a single element that is isomorphic to the trivial group. Its character table is given below. C_1 1 1 1

A tree with its nodes labeled. The number of labeled trees on n nodes is n^(n-2), the first few values of which are 1, 1, 3, 16, 125, 1296, ... (OEIS A000272). Cayley (1889) ...

The Laplace-Carson transform F of a real-valued function f is an integral transform defined by the formula F(p)=pint_0^inftye^(-pt)f(t)dt. (1) In most cases, the function F ...