Goldbach%20conjecture
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11: 17.14 Constant Term Identities
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Zeilberger–Bressoud Theorem (Andrews’ -Dyson Conjecture)
… βΊMacdonald (1982) includes extensive conjectures on generalizations of (17.14.1) to root systems. These conjectures were proved in Cherednik (1995), Habsieger (1986), and Kadell (1994); see also Macdonald (1998). …12: 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.
13: 23 Weierstrass Elliptic and Modular
Functions
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14: 9.9 Zeros
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9.9.6
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9.9.7
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9.9.8
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9.9.9
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βΊFor error bounds for the asymptotic expansions of , , , and see Pittaluga and Sacripante (1991), and a conjecture given in Fabijonas and Olver (1999).
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15: Bibliography
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Exact linearization of a Painlevé transcendent.
Phys. Rev. Lett. 38 (20), pp. 1103–1106.
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On the degrees of irreducible factors of higher order Bernoulli polynomials.
Acta Arith. 62 (4), pp. 329–342.
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Application of the combined nonlinear-condensation transformation to problems in statistical analysis and theoretical physics.
Comput. Phys. Comm. 150 (1), pp. 1–20.
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Repeated integrals and derivatives of Bessel functions.
SIAM J. Math. Anal. 20 (1), pp. 169–175.
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Plane partitions. III. The weak Macdonald conjecture.
Invent. Math. 53 (3), pp. 193–225.
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16: Bibliography D
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A proof of the Bieberbach conjecture.
Acta Math. 154 (1-2), pp. 137–152.
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Recherches analytiques sur la théorie des nombres premiers. Première partie. La fonction de Riemann et les nombres premiers en général, suivi d’un Appendice sur des réflexions applicables à une formule donnée par Riemann.
Ann. Soc. Sci. Bruxelles 20, pp. 183–256 (French).
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Recherches analytiques sur la théorie des nombres premiers. Deuxième partie. Les fonctions de Dirichlet et les nombres premiers de la forme linéaire
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Ann. Soc. Sci. Bruxelles 20, pp. 281–397 (French).
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Complex zeros of cylinder functions.
Math. Comp. 20 (94), pp. 215–222.
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Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions.
SIAM J. Math. Anal. 20 (3), pp. 744–760.
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17: 18.40 Methods of Computation
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βΊResults of low ( to decimal digits) precision for are easily obtained for to .
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βΊAn alternate, and highly efficient, approach follows from the derivative rule conjecture, see Yamani and Reinhardt (1975), and references therein, namely that
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18: 36 Integrals with Coalescing Saddles
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19: GergΕ Nemes
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βΊAs of September 20, 2021, Nemes performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 25 Zeta and Related Functions.
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20: Wolter Groenevelt
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βΊAs of September 20, 2022, Groenevelt performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 18 Orthogonal Polynomials.
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