Euler%E2%80%93Fermat%20theorem
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21: Bibliography K
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A proof of the -Macdonald-Morris conjecture for
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Mem. Amer. Math. Soc. 108 (516), pp. vi+80.
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Linear convergence and the bisection algorithm.
Amer. Math. Monthly 93 (1), pp. 48–51.
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A general addition theorem for spheroidal wave functions.
SIAM J. Math. Anal. 4 (1), pp. 149–160.
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Computation of tangent, Euler, and Bernoulli numbers.
Math. Comp. 21 (100), pp. 663–688.
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A new proof of a Paley-Wiener type theorem for the Jacobi transform.
Ark. Mat. 13, pp. 145–159.
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22: 24.20 Tables
§24.20 Tables
… ►Wagstaff (1978) gives complete prime factorizations of and for and , respectively. …23: 12.12 Integrals
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12.12.1
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12.12.2
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12.12.3
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12.12.4
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►For compendia of integrals see Erdélyi et al. (1953b, v. 2, pp. 121–122), Erdélyi et al. (1954a, b, v. 1, pp. 60–61, 115, 210–211, and 336;
v. 2, pp. 76–80, 115, 151, 171, and 395–398), Gradshteyn and Ryzhik (2000, §7.7), Magnus et al. (1966, pp. 330–331), Marichev (1983, pp. 190–191), Oberhettinger (1974, pp. 144–145), Oberhettinger (1990, pp. 106–108 and 192), Oberhettinger and Badii (1973, pp. 181–185), Prudnikov et al. (1986b, pp. 36–37, 155–168, 243–246, 289–290, 327–328, 419–420, and 619), Prudnikov et al. (1992a, §3.11), and Prudnikov et al. (1992b, §3.11).
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24: 5.5 Functional Relations
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5.5.1
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5.5.3
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5.5.5
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§5.5(iv) Bohr–Mollerup Theorem
►If a positive function on satisfies , , and is convex (see §1.4(viii)), then .25: 27.4 Euler Products and Dirichlet Series
§27.4 Euler Products and Dirichlet Series
►The fundamental theorem of arithmetic is linked to analysis through the concept of the Euler product. …In this case the infinite product on the right (extended over all primes ) is also absolutely convergent and is called the Euler product of the series. If is completely multiplicative, then each factor in the product is a geometric series and the Euler product becomes … ►Euler products are used to find series that generate many functions of multiplicative number theory. …26: 27.8 Dirichlet Characters
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►For any character , if and only if , in which case the Euler–Fermat theorem (27.2.8) implies .
There are exactly different characters (mod ), which can be labeled as .
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27.8.6
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27: 24.3 Graphs
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28: 5.11 Asymptotic Expansions
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►The scaled gamma function is defined in (5.11.3) and its main property is as in the sector .
Wrench (1968) gives exact values of up to .
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5.11.12
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5.11.13
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5.11.19
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