Types of Theorem

In mathematics, the Abel–Jacobi map is a construction of algebraic geometry which relates an algebraic curve to its Jacobian variety. In Riemannian geometry, it is a more general construction mapping a manifold to its Jacobi torus. The name derives from the theorem of Abel and Jacobi that two effective divisors are linearly equivalent if and only if they are indistinguishable under the Abel–Jacobi map.

12.2 Combinations and the Binomial Theorem 711 Expanding a Power of a Binomial Sum Expand (u + v2)3. SOLUTION (u + v2)3= 3C 0u 3(v2)0+ 3C 1u 2(v)1+ 3C 2u 1(v 2) + 3C 3u 0(v2)3 = u3+ 3u2v2+ 3uv4+ v6. . . . . . . . . . To expand a power of a binomial difference, you can rewrite the binomial as a sum. The resulting expansion will have terms whose signs alternate between + and º.

In mathematics, Abel's theorem for power series relates a limit of a power series to the sum of its coefficients. ... Complex Analysis (Third ed.).

The utility of Abel's theorem is that it allows us to find the limit of a power series as its argument (i.e. ) approaches 1 from below, even in cases where the radius of convergence, , of the power series is equal to 1 and we cannot be sure whether the limit should be finite or not.

Abelian and Tauberian Theorems: Philosophy Bent E. Petersen Math 515 Fall 1998 Next quarter, in Mth 516, we will discuss the Tauberian theorem of Ikehara and Landau and its connection with the prime number theorem (among other things). The notion of a Tauberian theorem is not all that precise { it is described by a philosophy rather than a de nition.

In algebraic geometry, a field of mathematics, the AF+BG theorem (also known as Max Noether's fundamental theorem) is a result of Max Noether which describes when the equation of an algebraic curve in the complex projective plane can be written in terms of the equations of two other algebraic curves.

In mathematics, the ATS theorem is the theorem on the approximation of a trigonometric sum by a shorter one. The application of the ATS theorem in certain problems of mathematical and theoretical physics can be very helpful.