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- Addition_theorem abstract "In mathematics, an addition theorem is a formula such as that for the exponential functionex + y = ex·ey that expresses, for a particular function f, f(x + y) in terms of f(x) and f(y). Slightly more generally, as is the case with the trigonometric functions sin and cos, several functions may be involved; this is more apparent than real, in that case, since there cos is an algebraic function of sin (in other words, we usually take their functions both as defined on the unit circle).The scope of the idea of an addition theorem was fully explored in the nineteenth century, prompted by the discovery of the addition theorem for elliptic functions. To 'classify' addition theorems it is necessary to put some restriction on the type of function G admitted, such that F(x + y) = G(F(x), F(y)).In this identity one can assume that F and G are vector-valued (have several components). An algebraic addition theorem is one in which G can be taken to be a vector of polynomials, in some set of variables. The conclusion of the mathematicians of the time was that the theory of abelian functions essentially exhausted the interesting possibilities: considered as a functional equation to be solved with polynomials, or indeed rational functions or algebraic functions, there were no further types of solution. In more contemporary language this appears as part of the theory of algebraic groups, dealing with commutative groups. The connected, projective variety examples are indeed exhausted by abelian functions, as is shown by a number of results characterising an abelian variety by rather weak conditions on its group law. The so-called quasi-abelian functions are all known to come from extensions of abelian varieties by commutative affine group varieties. Therefore the old conclusions about the scope of global algebraic addition theorems can be said to hold. A more modern aspect is the theory of formal groups.".
- Addition_theorem wikiPageID "973852".
- Addition_theorem wikiPageLength "2545".
- Addition_theorem wikiPageOutDegree "19".
- Addition_theorem wikiPageRevisionID "543841749".
- Addition_theorem wikiPageWikiLink Abelian_variety.
- Addition_theorem wikiPageWikiLink Algebraic_function.
- Addition_theorem wikiPageWikiLink Algebraic_group.
- Addition_theorem wikiPageWikiLink Category:Theorems_in_algebra.
- Addition_theorem wikiPageWikiLink Category:Theorems_in_algebraic_geometry.
- Addition_theorem wikiPageWikiLink Elliptic_function.
- Addition_theorem wikiPageWikiLink Exponential_function.
- Addition_theorem wikiPageWikiLink Formal_group.
- Addition_theorem wikiPageWikiLink Functional_equation.
- Addition_theorem wikiPageWikiLink Mathematics.
- Addition_theorem wikiPageWikiLink Polynomial.
- Addition_theorem wikiPageWikiLink Projective_variety.
- Addition_theorem wikiPageWikiLink Quasi-abelian_function.
- Addition_theorem wikiPageWikiLink Rational_function.
- Addition_theorem wikiPageWikiLink Timeline_of_abelian_varieties.
- Addition_theorem wikiPageWikiLink Trigonometric_functions.
- Addition_theorem wikiPageWikiLink Unit_circle.
- Addition_theorem wikiPageWikiLinkText "Addition theorem".
- Addition_theorem wikiPageWikiLinkText "addition theorem".
- Addition_theorem id "A/a110350".
- Addition_theorem title "Addition theorems in the theory of special functions".
- Addition_theorem wikiPageUsesTemplate Template:About.
- Addition_theorem wikiPageUsesTemplate Template:Springer.
- Addition_theorem subject Category:Theorems_in_algebra.
- Addition_theorem subject Category:Theorems_in_algebraic_geometry.
- Addition_theorem hypernym Formula.
- Addition_theorem type Agent.
- Addition_theorem type Theorem.
- Addition_theorem comment "In mathematics, an addition theorem is a formula such as that for the exponential functionex + y = ex·ey that expresses, for a particular function f, f(x + y) in terms of f(x) and f(y).".
- Addition_theorem label "Addition theorem".
- Addition_theorem sameAs Q282331.
- Addition_theorem sameAs 加法定理.
- Addition_theorem sameAs m.03vr7z.
- Addition_theorem sameAs Q282331.
- Addition_theorem wasDerivedFrom Addition_theorem?oldid=543841749.
- Addition_theorem isPrimaryTopicOf Addition_theorem.