induced%20modulus
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11: 25.3 Graphics
12: 36.5 Stokes Sets
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►The Stokes set consists of the rays in the complex -plane.
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36.5.4
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36.5.7
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►For , there are two solutions , provided that .
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►This consists of three separate cusp-edged sheets connected to the cusp-edged sheets of the bifurcation set, and related by rotation about the -axis by .
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13: 25.12 Polylogarithms
14: 10.3 Graphics
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§10.3(i) Real Order and Variable
►For the modulus and phase functions , , , and see §10.18. … ► … ► … ► …15: 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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►Gauss and Legendre conjectured that is asymptotic to as :
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16: 8 Incomplete Gamma and Related
Functions
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17: 28 Mathieu Functions and Hill’s Equation
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18: 7.23 Tables
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Abramowitz and Stegun (1964, Chapter 7) includes , , , 10D; , , 8S; , , 7D; , , , 6S; , , 10D; , , 9D; , , , 7D; , , , , 15D.
Zhang and Jin (1996, pp. 637, 639) includes , , , 8D; , , , 8D.
Zhang and Jin (1996, pp. 638, 640–641) includes the real and imaginary parts of , , , 7D and 8D, respectively; the real and imaginary parts of , , , 8D, together with the corresponding modulus and phase to 8D and 6D (degrees), respectively.
19: 8.26 Tables
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Khamis (1965) tabulates for , to 10D.
Abramowitz and Stegun (1964, pp. 245–248) tabulates for , to 7D; also for , to 6S.
Pagurova (1961) tabulates for , to 4-9S; for , to 7D; for , to 7S or 7D.
Zhang and Jin (1996, Table 19.1) tabulates for , to 7D or 8S.
20: 23 Weierstrass Elliptic and Modular
Functions
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