addition theorems
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31—38 of 38 matching pages
31: Errata
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►We now include Markov’s Theorem.
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Chapter 5 Addition
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Chapter 10 Additions
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Additions
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Additions
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Equation (5.2.9).
Equation (16.16.5_5).
Equation (4.13.5_3) (suggested by Warren Smith on 2023-08-10).
32: 1.10 Functions of a Complex Variable
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Picard’s Theorem
… ►§1.10(iv) Residue Theorem
… ►In addition, … ►Rouché’s Theorem
… ►Lagrange Inversion Theorem
…33: 10.22 Integrals
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►Hankel’s inversion theorem is given by
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10.22.77
►Sufficient conditions for the validity of (10.22.77) are that when , or that and when ; see Titchmarsh (1986a, Theorem 135, Chapter 8) and Akhiezer (1988, p. 62).
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10.22.78
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10.22.79
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34: 1.12 Continued Fractions
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Pringsheim’s Theorem
… ►Van Vleck’s Theorem
… ►The continued fraction converges iff, in addition, …35: 2.1 Definitions and Elementary Properties
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►For example, if is analytic for all sufficiently large in a sector and as in , being real, then as in any closed sector properly interior to and with the same vertex (Ritt’s theorem).
This result also holds with both ’s replaced by ’s.
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►These include addition, subtraction, multiplication, and division.
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36: 18.17 Integrals
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►For addition formulas corresponding to (18.17.5) and (18.17.6) see (18.18.8) and (18.18.9), respectively.
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