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1: Bibliography D
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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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The constrained quantum mechanical harmonic oscillator.
Proc. Cambridge Philos. Soc. 62, pp. 277–286.
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Handbuch der Laplace-Transformation. Bd. II. Anwendungen der Laplace-Transformation. 1. Abteilung.
Birkhäuser Verlag, Basel und Stuttgart (German).
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Complex zeros of cylinder functions.
Math. Comp. 20 (94), pp. 215–222.
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2: Bibliography H
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Algorithm 55: Complete elliptic integral of the first kind.
Comm. ACM 4 (4), pp. 180.
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Algorithm 56: Complete elliptic integral of the second kind.
Comm. ACM 4 (4), pp. 180–181.
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Coulomb Wave Functions.
In Handbuch der Physik, Bd. 41/1, S. Flügge (Ed.),
pp. 408–465.
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Asymptotic expansions of Mathieu functions in wave mechanics.
J. Comput. Phys. 21 (3), pp. 319–325.
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3: 20 Theta Functions
Chapter 20 Theta Functions
…4: Tom M. Apostol
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►Apostol was born on August 20, 1923.
He received his bachelor of science in chemical engineering in 1944 and a master’s degree in mathematics in 1946, both from the University of Washington, Seattle.
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►He was also a coauthor of three textbooks written to accompany the physics telecourse The Mechanical Universe …and Beyond.
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5: 8 Incomplete Gamma and Related
Functions
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6: 28 Mathieu Functions and Hill’s Equation
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7: 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.
8: 23 Weierstrass Elliptic and Modular
Functions
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9: 36 Integrals with Coalescing Saddles
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10: Gergő Nemes
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►As 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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