relation%20to%20Anger%E2%80%93Weber%20functions
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21: 6.16 Mathematical Applications
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►Hence, if is fixed and , then , , or according as , , or ; compare (6.2.14).
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►Hence if and , then the limiting value of overshoots by approximately 18%.
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►If we assume Riemann’s hypothesis that all nonreal zeros of have real part of (§25.10(i)), then
…where is the number of primes less than or equal to
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22: 11.14 Tables
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Zhang and Jin (1996) tabulates and for and to 8D or 7S.
§11.14(iv) Anger–Weber Functions
►Bernard and Ishimaru (1962) tabulates and for and to 5D.
Jahnke and Emde (1945) tabulates for and to 4D.
§11.14(v) Incomplete Functions
…23: Bibliography B
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Pionic atoms.
Annual Review of Nuclear and Particle Science 20, pp. 467–508.
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A short table of the functions
, from
to
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Phil. Mag. Series 7 20, pp. 343–347.
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Tables Relating to the Radial Mathieu Functions. Vol. 1: Functions of the First Kind.
U.S. Government Printing Office, Washington, D.C..
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Tables Relating to the Radial Mathieu Functions. Vol. 2: Functions of the Second Kind.
U.S. Government Printing Office, Washington, D.C..
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Bessel functions and modular relations of higher type and hyperbolic differential equations.
Comm. Sém. Math. Univ. Lund [Medd. Lunds Univ. Mat. Sem.] 1952 (Tome Supplementaire), pp. 12–20.
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24: Bibliography
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Some series of the zeta and related functions.
Analysis (Munich) 18 (2), pp. 131–144.
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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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Dirichlet series related to the Riemann zeta function.
J. Number Theory 19 (1), pp. 85–102.
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Integral equations and relations for Lamé functions.
Quart. J. Math. Oxford Ser. (2) 15, pp. 103–115.
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25: 25 Zeta and Related Functions
Chapter 25 Zeta and Related Functions
…26: 8.26 Tables
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Khamis (1965) tabulates for , to 10D.
Pearson (1965) tabulates the function () for , to 7D, where rounds off to 1 to 7D; also for , to 5D.
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.