Continued Fractions, Convergence Theory. Vol. 1, 2nd Editions. Loretzen, Waadeland. Atlantis Press. 2008

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1.3.1 Expansions of functions 25 1.3 Rational approximation to functions 1.3.1 Expansions of functions Example 10. In this book √ ... shall always denote the principal branch of the square root; that is, − π 2 < arg √ ... ≤ π .Forz ∈ D := {z ∈ C; | arg(1 + z)| 1. Its partial sums are σ 1 (z) = 1 2 z, σ 2(z) = 1 2 z − 1 8 z2 , σ 3 (z) = 1 2 z − 1 8 z2 + 1 16 z3 ,... ,
26 Chapter 1: Introductory examples and they are polynomial approximations to √ 1+z −1 for z in the unit disk D := {z ∈ C; |z| < 1}. The approximants f n (z) in Example 10 approximate √ 1+z − 1 in a much larger region, D := {z ∈ C; | arg(1 + z)|
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266 Appendix A: Some continued frac
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296 Bibliography [Bear04] A. F. Bea
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298 Bibliography [Glai74] J. W. L.
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300 Bibliography [JoTW82] W. B. Jon
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302 Bibliography [Mind69] F. Mindin
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304 Bibliography [ThWa80b] W. J. Th
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Index (a) n Pochhammer symbol, 27 A
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308 Index moment problem, 40, 41 od
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Continued Fractions, Convergence Theory. Vol. 1, 2nd Editions. Loretzen, Waadeland. Atlantis Press. 2008

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