TY - BOOK AU - Mahler,Kurt AU - Diviš,B. AU - Veque,W.J. ED - SpringerLink (Online service) TI - Lectures on Transcendental Numbers T2 - Lecture Notes in Mathematics, SN - 9783540379812 AV - QA241-247.5 U1 - 512.7 23 PY - 1976/// CY - Berlin, Heidelberg PB - Springer Berlin Heidelberg, Imprint: Springer KW - Mathematics KW - Number theory KW - Number Theory N1 - Existence and first properties of transcendental numbers -- Convergent laurent series and formal laurent series -- First results on the values of analytic functions at algebraic points -- Linear differental equations: The lemmas of Shidlovski -- Linear differential equations: A lower bound for the rank of the values of finitely many siegel E-functions at algebraic points -- Linear differential equations: Shidlovski's theorems on the transcendency and algebraic independence of values of siegel E-functions -- Applications of Shidlovski's main theorems to special functions -- Formal power series as solutions of algebraic differential equations UR - http://dx.doi.org/10.1007/BFb0081107 ER -