Ebook: Lectures on Transcendental Numbers

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Content:
Front Matter....Pages I-XXI
Existence and first properties of transcendental numbers....Pages 1-28
Convergent laurent series and formal laurent series....Pages 29-44
First results on the values of analytic functions at algebraic points....Pages 45-59
Linear differental equations: The lemmas of Shidlovski....Pages 60-89
Linear differential equations: A lower bound for the rank of the values of finitely many siegel E-functions at algebraic points....Pages 90-114
Linear differential equations: Shidlovski's theorems on the transcendency and algebraic independence of values of siegel E-functions....Pages 115-144
Applications of Shidlovski's main theorems to special functions....Pages 145-184
Formal power series as solutions of algebraic differential equations....Pages 185-212
Back Matter....Pages 213-254

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Content:
Front Matter....Pages I-XXI
Existence and first properties of transcendental numbers....Pages 1-28
Convergent laurent series and formal laurent series....Pages 29-44
First results on the values of analytic functions at algebraic points....Pages 45-59
Linear differental equations: The lemmas of Shidlovski....Pages 60-89
Linear differential equations: A lower bound for the rank of the values of finitely many siegel E-functions at algebraic points....Pages 90-114
Linear differential equations: Shidlovski's theorems on the transcendency and algebraic independence of values of siegel E-functions....Pages 115-144
Applications of Shidlovski's main theorems to special functions....Pages 145-184
Formal power series as solutions of algebraic differential equations....Pages 185-212
Back Matter....Pages 213-254
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