principal%20branch
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1—10 of 13 matching pages
1: 15.10 Hypergeometric Differential Equation
2: 32.8 Rational Solutions
3: 6.16 Mathematical Applications
4: 25.12 Polylogarithms
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►Other notations and names for include (Kölbig et al. (1970)), Spence function (’t Hooft and Veltman (1979)), and (Maximon (2003)).
►In the complex plane has a branch point at .
The principal branch has a cut along the interval and agrees with (25.12.1) when ; see also §4.2(i).
The remainder of the equations in this subsection apply to principal branches.
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5: 27.2 Functions
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►Euclid’s Elements (Euclid (1908, Book IX, Proposition 20)) gives an elegant proof that there are infinitely many primes.
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27.2.3
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27.2.4
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27.2.14
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6: 5.11 Asymptotic Expansions
7: 10.75 Tables
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Achenbach (1986) tabulates , , , , , 20D or 18–20S.
Kerimov and Skorokhodov (1985a) tabulates 5 (nonreal) complex conjugate pairs of zeros of the principal branches of and for , 8D.
Kerimov and Skorokhodov (1985b) tabulates 50 zeros of the principal branches of and , 8D.
Bickley et al. (1952) tabulates or , or , , (.01 or .1) 10(.1) 20, 8S; , , , or , 10S.
Kerimov and Skorokhodov (1984b) tabulates all zeros of the principal values of and , for , 9S.