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• Lindemann–Weierstrass_theorem abstract "In transcendental number theory, the Lindemann–Weierstrass theorem is a result that is very useful in establishing the transcendence of numbers. It states that if α1, ..., αn are algebraic numbers which are linearly independent over the rational numbers ℚ, then eα1, ..., eαn are algebraically independent over ℚ; in other words the extension field ℚ(eα1, ..., eαn) has transcendence degree n over ℚ. An equivalent formulation (Baker 1975, Chapter 1, Theorem 1.4), is the following: If α1, ..., αn are distinct algebraic numbers, then the exponentials eα1, ..., eαn are linearly independent over the algebraic numbers. This equivalence transforms a linear relation over the algebraic numbers into an algebraic relation over ℚ; by using the fact that a symmetric polynomial whose arguments are all conjugates of one another gives a rational number.The theorem is named for Ferdinand von Lindemann and Karl Weierstrass. Lindemann proved in 1882 that eα is transcendental for every non-zero algebraic number α, thereby establishing that π is transcendental (see below). Weierstrass proved the above more general statement in 1885.The theorem, along with the Gelfond–Schneider theorem, is extended by Baker's theorem, and all of these are further generalized by Schanuel's conjecture.".
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• Lindemann–Weierstrass_theorem wikiPageWikiLink Algebraic_independence.
• Lindemann–Weierstrass_theorem wikiPageWikiLink Algebraic_number.
• Lindemann–Weierstrass_theorem wikiPageWikiLink Bakers_theorem.
• Lindemann–Weierstrass_theorem wikiPageWikiLink Category:Articles_containing_proofs.
• Lindemann–Weierstrass_theorem wikiPageWikiLink Category:E_(mathematical_constant).
• Lindemann–Weierstrass_theorem wikiPageWikiLink Category:Exponentials.
• Lindemann–Weierstrass_theorem wikiPageWikiLink Category:Pi.
• Lindemann–Weierstrass_theorem wikiPageWikiLink Category:Theorems_in_number_theory.
• Lindemann–Weierstrass_theorem wikiPageWikiLink Category:Transcendental_numbers.
• Lindemann–Weierstrass_theorem wikiPageWikiLink Charles_Hermite.
• Lindemann–Weierstrass_theorem wikiPageWikiLink Coefficient.
• Lindemann–Weierstrass_theorem wikiPageWikiLink Conjugate_(algebra).
• Lindemann–Weierstrass_theorem wikiPageWikiLink David_Hilbert.
• Lindemann–Weierstrass_theorem wikiPageWikiLink Degree_of_a_polynomial.
• Lindemann–Weierstrass_theorem wikiPageWikiLink E_(mathematical_constant).
• Lindemann–Weierstrass_theorem wikiPageWikiLink Eulers_identity.
• Lindemann–Weierstrass_theorem wikiPageWikiLink Ferdinand_von_Lindemann.
• Lindemann–Weierstrass_theorem wikiPageWikiLink Field_extension.
• Lindemann–Weierstrass_theorem wikiPageWikiLink Gelfond–Schneider_theorem.
• Lindemann–Weierstrass_theorem wikiPageWikiLink Hyperbolic_function.
• Lindemann–Weierstrass_theorem wikiPageWikiLink Integer.
• Lindemann–Weierstrass_theorem wikiPageWikiLink Integration_by_parts.
• Lindemann–Weierstrass_theorem wikiPageWikiLink J-invariant.
• Lindemann–Weierstrass_theorem wikiPageWikiLink Karl_Weierstrass.
• Lindemann–Weierstrass_theorem wikiPageWikiLink Linear_independence.
• Lindemann–Weierstrass_theorem wikiPageWikiLink Modular_form.
• Lindemann–Weierstrass_theorem wikiPageWikiLink Nome_(mathematics).
• Lindemann–Weierstrass_theorem wikiPageWikiLink P-adic_exponential_function.
• Lindemann–Weierstrass_theorem wikiPageWikiLink P-adic_number.
• Lindemann–Weierstrass_theorem wikiPageWikiLink Pi.
• Lindemann–Weierstrass_theorem wikiPageWikiLink Prime_number.
• Lindemann–Weierstrass_theorem wikiPageWikiLink Proof_by_contradiction.
• Lindemann–Weierstrass_theorem wikiPageWikiLink Rational_number.
• Lindemann–Weierstrass_theorem wikiPageWikiLink Schanuels_conjecture.
• Lindemann–Weierstrass_theorem wikiPageWikiLink Symmetric_polynomial.
• Lindemann–Weierstrass_theorem wikiPageWikiLink Transcendence_degree.
• Lindemann–Weierstrass_theorem wikiPageWikiLink Transcendental_number.
• Lindemann–Weierstrass_theorem wikiPageWikiLink Transcendental_number_theory.
• Lindemann–Weierstrass_theorem wikiPageWikiLink Unit_disk.
• Lindemann–Weierstrass_theorem wikiPageWikiLinkText "Lindemann–Weierstrass theorem".
• Lindemann–Weierstrass_theorem wikiPageWikiLinkText "Lindemann–Weierstrass theorem#Transcendence_of_e_and_π".
• Lindemann–Weierstrass_theorem wikiPageWikiLinkText "Lindemann–Weierstrass_theorem#Transcendence_of_e_and_.CF.80".
• Lindemann–Weierstrass_theorem wikiPageWikiLinkText "Proof that e is transcendental".
• Lindemann–Weierstrass_theorem wikiPageWikiLinkText "Transcendence of ''e'' and π".
• Lindemann–Weierstrass_theorem wikiPageWikiLinkText "transcendental as well".
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• Lindemann–Weierstrass_theorem subject Category:Articles_containing_proofs.
• Lindemann–Weierstrass_theorem subject Category:E_(mathematical_constant).
• Lindemann–Weierstrass_theorem subject Category:Exponentials.
• Lindemann–Weierstrass_theorem subject Category:Pi.
• Lindemann–Weierstrass_theorem subject Category:Theorems_in_number_theory.
• Lindemann–Weierstrass_theorem subject Category:Transcendental_numbers.
• Lindemann–Weierstrass_theorem hypernym Result.
• Lindemann–Weierstrass_theorem type Diacritic.
• Lindemann–Weierstrass_theorem type Field.
• Lindemann–Weierstrass_theorem type Proof.
• Lindemann–Weierstrass_theorem type Ratio.
• Lindemann–Weierstrass_theorem type Redirect.
• Lindemann–Weierstrass_theorem type Theorem.
• Lindemann–Weierstrass_theorem comment "In transcendental number theory, the Lindemann–Weierstrass theorem is a result that is very useful in establishing the transcendence of numbers. It states that if α1, ..., αn are algebraic numbers which are linearly independent over the rational numbers ℚ, then eα1, ..., eαn are algebraically independent over ℚ; in other words the extension field ℚ(eα1, ..., eαn) has transcendence degree n over ℚ.".
• Lindemann–Weierstrass_theorem label "Lindemann–Weierstrass theorem".
• Lindemann–Weierstrass_theorem sameAs Q1572474.
• Lindemann–Weierstrass_theorem sameAs مبرهنة_ليندمان-ويرستراس.
• Lindemann–Weierstrass_theorem sameAs Teorema_de_Lindemann-Weierstrass.
• Lindemann–Weierstrass_theorem sameAs Satz_von_Lindemann-Weierstraß.
• Lindemann–Weierstrass_theorem sameAs Teorema_de_Lindemann–Weierstrass.
• Lindemann–Weierstrass_theorem sameAs Théorème_de_Lindemann-Weierstrass.
• Lindemann–Weierstrass_theorem sameAs משפט_לינדמן-ויירשטראס.
• Lindemann–Weierstrass_theorem sameAs Teorema_di_Lindemann-Weierstrass.
• Lindemann–Weierstrass_theorem sameAs リンデマンの定理.
• Lindemann–Weierstrass_theorem sameAs Stelling_van_Lindemann-Weierstrass.
• Lindemann–Weierstrass_theorem sameAs Teorema_de_Lindemann–Weierstrass.
• Lindemann–Weierstrass_theorem sameAs m.01z0m2.
• Lindemann–Weierstrass_theorem sameAs Теорема_Линдемана_—_Вейерштрасса.
• Lindemann–Weierstrass_theorem sameAs Lindemann-Weierstrassov_izrek.
• Lindemann–Weierstrass_theorem sameAs Q1572474.
• Lindemann–Weierstrass_theorem sameAs 林德曼-魏尔斯特拉斯定理.
• Lindemann–Weierstrass_theorem wasDerivedFrom Lindemann–Weierstrass_theorem?oldid=696274416.
• Lindemann–Weierstrass_theorem isPrimaryTopicOf Lindemann–Weierstrass_theorem.