Classical Constants and Functions: Computations and Continued Fraction Expansions

D. V. Chudnovsky and G. V. Chudnovsky
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D. V. Chudnovsky: Columbia University, Department of Mathematics
G. V. Chudnovsky: Columbia University, Department of Mathematics

Chapter 2 in Number Theory, 1991, pp 13-74 from Springer

Abstract: Abstract This lecture focuses on the arithmetic (diophantine) nature of constants and functions of classical analysis and geometry. We study power series and continued fraction expansion of functions, and related fixed radix and continued fraction expansions of numbers. We try to classify all cases of closed form expressions of continued fraction expansions and present the corresponding identities. At the same time we want to understand what happens when no closed form expression exists.

Keywords: Riemann Surface; Orthogonal Polynomial; Linear Differential Equation; Elliptic Function; Iterate Logarithm (search for similar items in EconPapers)
Date: 1991
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4757-4158-2_2

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DOI: 10.1007/978-1-4757-4158-2_2

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