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A Tauberian theorem is a theorem that deduces the convergence of an series on the basis of the properties of the function it defines and any kind of auxiliary hypothesis ...

Abstractly, the tensor direct product is the same as the vector space tensor product. However, it reflects an approach toward calculation using coordinates, and indices in ...

A lattice polygon formed by a three-choice walk. The anisotropic perimeter and area generating function G(x,y,q)=sum_(m>=1)sum_(n>=1)sum_(a>=a)C(m,n,a)x^my^nq^a, where ...

The triangle function is the function Lambda(x) = {0 |x|>=1; 1-|x| |x|<1 (1) = Pi(x)*Pi(x) (2) = Pi(x)*H(x+1/2)-Pi(x)*H(x-1/2), (3) where Pi(x) is the rectangle function, ...

A square matrix A is said to be unipotent if A-I, where I is an identity matrix is a nilpotent matrix (defined by the property that A^n is the zero matrix for some positive ...

A unit ring is a ring with a multiplicative identity. It is therefore sometimes also known as a "ring with identity." It is given by a set together with two binary operators ...

There are a number of algebraic identities involving sets of four vectors. An identity known as Lagrange's identity is given by (AxB)·(CxD)=(A·C)(B·D)-(A·D)(B·C) (1) ...

A zonal harmonic is a spherical harmonic of the form P_l(costheta), i.e., one which reduces to a Legendre polynomial (Whittaker and Watson 1990, p. 302). These harmonics are ...

The ordinary differential equation y=xf(y^')+g(y^'), where y^'=dy/dx and f and g are given functions. This equation is sometimes also known as Lagrange's equation (Zwillinger ...

A q-analog of Gauss's theorem due to Jacobi and Heine, _2phi_1(a,b;c;q,c/(ab))=((c/a;q)_infty(c/b;q)_infty)/((c;q)_infty(c/(ab);q)_infty) (1) for |c/(ab)|<1 (Gordon and ...