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{{About|addition theorems in general|specific addition theorems for trigonometric functions|angle addition formulas}} ...of the addition theorem for [[elliptic function]]s. To "classify" addition theorems it is necessary to put some restriction on the type of function ''G'' admit ...

An interval polynomial is the family of all polynomials ...of the family are stable) if and only if the four so-called '''Kharitonov polynomials''' ...

...rix), a tridiagonal symmetric matrix appearing in the theory of orthogonal polynomials * [[Jacobi polynomials]], a class of orthogonal polynomials ...

...matics]], the '''Brauer–Nesbitt theorem''' can refer to several different theorems proved by [[Richard Brauer]] and [[Cecil J. Nesbitt]] in the [[representati .../math> or <math>char(E)>n</math>, then the condition on the characteristic polynomials can be changed to the condition that Tr<math>\rho_1(g)</math>=Tr<math>\rho_ ...

'''Chebyshev's theorem''' is any of several theorems proven by Russian mathematician [[Pafnuty Chebyshev]]. * [[Chebyshev's sum inequality]], about sums and products of decreasing sequences ...

...d Wright}}</ref> Some of these are [[Classification theorem|classification theorems]] of objects which are mainly dealt with in the field. For instance, the [[ ==Fundamental theorems of mathematical topics== ...

{{for|Lagrange's other theorems|Lagrange's theorem (disambiguation)}} ...Prime number|prime]] ''p''. More precisely, it states that for all integer polynomials <math>\textstyle f \in \mathbb{Z}[x]</math>, either: ...

..._1,\ldots,X_n)</math> and <math>g(X_2, \ldots,X_n)</math> are multivariate polynomials and <math>g</math> is independent of <math>X_1</math>, then <math>X_1 - g(X ==Factorization of polynomials== ...

'''Mergelyan's theorem''' is a result from approximation by polynomials in [[complex analysis]] proved by the [[Armenian SSR|Armenian]] [[mathemat | title = Mergelyan's and Arakelian's theorems for manifold-valued maps ...

== Statement of the theorems == ...math>\{f_j\}_{j=1}^r\subseteq\mathbb{F}[X_1,\ldots,X_n]</math> be a set of polynomials such that the number of variables satisfies ...

{{short description|Result in number theory, concerning irreducible polynomials}} ...of a proper subset of the variables to rational numbers such that all the polynomials remain irreducible. This theorem is a prominent theorem in number theory. ...

...lynomials with this property are called [[stable polynomial|Hurwitz stable polynomials]]. The Routh–Hurwitz theorem is important in [[dynamical system]]s and [[c ...inary unit]] and {{math|''c''}} is a [[real number]]). Let us define real polynomials {{math|''P''₀(''y'')}} and {{math|''P''₁(''y'')}} by ...

{{Short description|Sequence of polynomials}} ...polynomials Q_n occasionally called Touchard polynomials|Bateman polynomials}} ...

...2/pdf12-1/uproots.pdf}}</ref> is an application of [[Euclidean division of polynomials]]. It states that, for every number <math>r</math>, any [[polynomial]] <mat ...[[Euclidean division of polynomials|Euclidean division]], which, given two polynomials {{math|''f''(''x'')}} (the dividend) and {{math|''g''(''x'')}} (the divisor ...

...e unfactorable into the product of lower-[[degree of a polynomial|degree]] polynomials with [[integer]] [[coefficient]]s. ...last1=Pólya |first1=George |last2=Szegő |first2=Gábor |title=Problems and theorems in analysis, volume 2 |publisher=Springer |year=2004 |volume=2 |isbn=978-3- ...

...e journal |first=Richard P. |last=Stanley |title=Combinatorial reciprocity theorems |journal=[[Advances in Mathematics]] |volume=14 |issue=2 |pages=194–253 |ye ...eciprocity theorem generalizes Ehrhart-Macdonald reciprocity for [[Ehrhart polynomials]] of rational [[Convex polytope|convex polytopes]]. ...

* Any of a number of [[fundamental theorems]] identified in mathematics, such as: ...Fundamental theorem of algebra]], a theorem regarding the factorization of polynomials ...

...us theorem) and the [[syzygy theorem]] (theorem on relations). These three theorems were the starting point of the interpretation of [[algebraic geometry]] in ...] is the set of the common [[root of a polynomial|zeros]] of finitely many polynomials. ...

* [[Reciprocity (electromagnetism)]], theorems relating sources and the resulting fields in classical electromagnetism ** [[Cubic reciprocity]], theorems that state conditions under which the congruence {{nowrap|''x''³ ...

The [[Legendre polynomials]] <math>P_n(x)</math> are solutions to the [[Sturm–Liouville theory|Sturm–L ...s (known in this case as a Fourier–Legendre series) involving the Legendre polynomials, so that ...