Search Results for ""

The Jacobi symbol (a/y)=chi(y) as a number theoretic character can be extended to the Kronecker symbol (f(a)/y)=chi^*(y) so that chi^*(y)=chi(y) whenever chi(y)!=0. When y is ...

Let K be a field of field characteristic 0 (e.g., the rationals Q) and let {u_n} be a sequence of elements of K which satisfies a difference equation of the form ...

sum_(k=0)^(infty)[((m)_k)/(k!)]^3 = 1+(m/1)^3+[(m(m+1))/(1·2)]^3+... (1) = (Gamma(1-3/2m))/([Gamma(1-1/2m)]^3)cos(1/2mpi), (2) where (m)_k is a Pochhammer symbol and Gamma(z) ...

Given a vector space V, its projectivization P(V), sometimes written P(V-0), is the set of equivalence classes x∼lambdax for any lambda!=0 in V-0. For example, complex ...

A generalization of the Gaussian sum. For p and q of opposite parity (i.e., one is even and the other is odd), Schaar's identity states ...

A link L is said to be splittable if a plane can be embedded in R^3 such that the plane separates one or more components of L from other components of L and the plane is ...

The nth central trinomial coefficient is defined as the coefficient of x^n in the expansion of (1+x+x^2)^n. It is therefore the middle column of the trinomial triangle, i.e., ...

A finite or infinite square matrix with rational entries. (If the matrix is infinite, all but a finite number of entries in each row must be 0.) The sum or product of two ...

An imaginary quadratic field is a quadratic field Q(sqrt(D)) with D<0. Special cases are summarized in the following table. D field members -1 Gaussian integer -3 Eisenstein ...

An integer kappa equal to 0 or 1 which vanishes iff the product manifold M^4×R can be given a smooth structure. Here, M^n is a compact connected topological four-manifold.