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3 matching pages
1: 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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►For other values of , is defined by analytic continuation.
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2: 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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3: 10.75 Tables
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Makinouchi (1966) tabulates all values of and in the interval , with at least 29S. These are for , 10, 20; , ; with and , except for .
Kerimov and Skorokhodov (1985a) tabulates 5 (nonreal) complex conjugate pairs of zeros of the principal branches of and for , 8D.
Parnes (1972) tabulates all zeros of the principal value of , for , 9D.
Leung and Ghaderpanah (1979), tabulates all zeros of the principal value of , for , 29S.
Kerimov and Skorokhodov (1984b) tabulates all zeros of the principal values of and , for , 9S.