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1: 23.9 Laurent and Other Power Series
§23.9 Laurent and Other Power Series
β–Ί
c 2 = 1 20 ⁒ g 2 ⁑ ,
2: 25.11 Hurwitz Zeta Function
β–ΊThe function ΞΆ ⁑ ( s , a ) was introduced in Hurwitz (1882) and defined by the series expansion … β–Ί
§25.11(iii) Representations by the Euler–Maclaurin Formula
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§25.11(iv) Series Representations
β–ΊFor other series expansions similar to (25.11.10) see Coffey (2008). … β–Ί
§25.11(x) Further Series Representations
3: Bibliography B
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  • G. Backenstoss (1970) Pionic atoms. Annual Review of Nuclear and Particle Science 20, pp. 467–508.
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  • K. L. Bell and N. S. Scott (1980) Coulomb functions (negative energies). Comput. Phys. Comm. 20 (3), pp. 447–458.
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  • B. C. Berndt (1975a) Character analogues of the Poisson and Euler-MacLaurin summation formulas with applications. J. Number Theory 7 (4), pp. 413–445.
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  • W. G. Bickley and J. Nayler (1935) A short table of the functions Ki n ⁒ ( x ) , from n = 1 to n = 16 . Phil. Mag. Series 7 20, pp. 343–347.
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  • W. G. Bickley (1935) Some solutions of the problem of forced convection. Philos. Mag. Series 7 20, pp. 322–343.
  • 4: Bibliography F
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  • FDLIBM (free C library)
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  • S. Fempl (1960) Sur certaines sommes des intégral-cosinus. Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).
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  • W. B. Ford (1960) Studies on Divergent Series and Summability & The Asymptotic Developments of Functions Defined by Maclaurin Series. Chelsea Publishing Co., New York.
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  • G. Freud (1969) On weighted polynomial approximation on the whole real axis. Acta Math. Acad. Sci. Hungar. 20, pp. 223–225.
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  • T. Fukushima (2012) Series expansions of symmetric elliptic integrals. Math. Comp. 81 (278), pp. 957–990.
  • 5: Bibliography S
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  • A. Sharples (1967) Uniform asymptotic forms of modified Mathieu functions. Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.
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  • A. Sidi (2004) Euler-Maclaurin expansions for integrals with endpoint singularities: A new perspective. Numer. Math. 98 (2), pp. 371–387.
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  • A. Sidi (2012a) Euler-Maclaurin expansions for integrals with arbitrary algebraic endpoint singularities. Math. Comp. 81 (280), pp. 2159–2173.
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  • A. Sidi (2012b) Euler-Maclaurin expansions for integrals with arbitrary algebraic-logarithmic endpoint singularities. Constr. Approx. 36 (3), pp. 331–352.
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  • F. Stenger (1993) Numerical Methods Based on Sinc and Analytic Functions. Springer Series in Computational Mathematics, Vol. 20, Springer-Verlag, New York.