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Irreducible orientable compact 3-manifolds have a canonical (up to isotopy) minimal collection of disjointly embedded incompressible tori such that each component of the ...

e^(izcostheta)=sum_(n=-infty)^inftyi^nJ_n(z)e^(intheta), where J_n(z) is a Bessel function of the first kind. The identity can also be written ...

Q_n^((alpha,beta))(x)=2^(-n-1)(x-1)^(-alpha)(x+1)^(-beta) ×int_(-1)^1(1-t)^(n+alpha)(1+t)^(n+beta)(x-t)^(-n-1)dt. In the exceptional case n=0, alpha+beta+1=0, a nonconstant ...

The Jacobi triple product is the beautiful identity product_(n=1)^infty(1-x^(2n))(1+x^(2n-1)z^2)(1+(x^(2n-1))/(z^2))=sum_(m=-infty)^inftyx^(m^2)z^(2m). (1) In terms of the ...

The Jacobian group of a one-dimensional linear series is given by intersections of the base curve with the Jacobian curve of itself and two curves cutting the series.

Let M_r be an r-rowed minor of the nth order determinant |A| associated with an n×n matrix A=a_(ij) in which the rows i_1, i_2, ..., i_r are represented with columns k_1, ...

The Jacobsthal polynomials are the w-polynomials obtained by setting p(x)=1 and q(x)=2x in the Lucas polynomial sequence. The first few Jacobsthal-Lucas polynomials are ...

Given a convex plane region with area A and perimeter p, then |N-A|<p, where N is the number of enclosed lattice points.

The Jerabek center X_(125) (center of the Jerabek hyperbola) lies on the nine-point circle. The Jerabek antipode is the antipode of this point on nine-point circle. It has ...

Using Clebsch-Aronhold notation, an algebraic curve satisfies xi_1^na_y^n+xi_1^(n-1)xi_2a_y^(n-1)a_x+1/2n(n-1)xi_1^(n-2)xi_2^2a_y^(n-2)a_x^2+... ...