Ads
related to: rational method coefficients table for math questions
Search results
Results from the WOW.Com Content Network
It is an open question what is the smallest number (,), such that any n-variate, non-negative polynomial of degree d can be written as sum of at most (,) square rational functions over the reals. An upper bound due to Pfister in 1967 is: [8]
In mathematics, the method of undetermined coefficients is an approach to finding a particular solution to certain nonhomogeneous ordinary differential equations and recurrence relations.
Ultimately if it is possible to show that no finite degree or size of coefficient is sufficient then the number must be transcendental. Since a number α is transcendental if and only if P(α) ≠ 0 for every non-zero polynomial P with integer coefficients, this problem can be approached by trying to find lower bounds of the form
In mathematics, "rational" is often used as a noun abbreviating "rational number". The adjective rational sometimes means that the coefficients are rational numbers. For example, a rational point is a point with rational coordinates (i.e., a point whose coordinates are rational numbers); a rational matrix is a matrix of rational numbers; a rational polynomial may be a polynomial with rational ...
In mathematics, Eisenstein's theorem, named after the German mathematician Gotthold Eisenstein, applies to the coefficients of any power series which is an algebraic function with rational number coefficients. Through the theorem, it is readily demonstrable, for example, that the exponential function must be a transcendental function.
It follows that the roots of a polynomial with real coefficients are mirror-symmetric with respect to the real axis. This can be extended to algebraic conjugation: the roots of a polynomial with rational coefficients are conjugate (that is, invariant) under the action of the Galois group of the polynomial. However, this symmetry can rarely be ...
In mathematics, Descartes' rule of signs, described by René Descartes in his La Géométrie, counts the roots of a polynomial by examining sign changes in its coefficients. The number of positive real roots is at most the number of sign changes in the sequence of polynomial's coefficients (omitting zero coefficients), and the difference ...
The problem addressed by the circle method is to force the issue of taking r = 1, by a good understanding of the nature of the singularities f exhibits on the unit circle. The fundamental insight is the role played by the Farey sequence of rational numbers, or equivalently by the roots of unity:
Ads
related to: rational method coefficients table for math questions