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214 lines
9.5 KiB
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214 lines
9.5 KiB
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References
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The following is a non-comprehensive list of works used in the development of mpmath
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or cited for examples or mathematical definitions used in this documentation.
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References not listed here can be found in the source code.
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in Engineering* 60:979-993, http://dx.doi.org/10.1002/nme.995
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inversion of the Laplace transform: Applications to Biology,
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Economics, Engineering, and Physics*. Elsevier.
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Scientists and Engineers*, Springer 1999
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Analytic Number Theory and Computational Complexity*,
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Wiley 1987
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Convergence of the Tanh-sinh Quadrature Rule.” (2006).
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Function", http://www.cecm.sfu.ca/personal/pborwein/PAPERS/P155.pdf
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Critical Strip, Math. Comp. 33 (1979) 1361--1372
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'On the Zeros of the Riemann Zeta Function in the Critical
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Strip. II', Math. Comp. 39 (1982) 681--688.
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Argument", Proc. Amer. Math. Soc., Vol. 114, No. 1 (Jan. 1992),
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pp.145-153
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and the Scalar One-Loop Three-point Integrals in Feynman
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Diagrams". http://arxiv.org/abs/hep-ph/0206081
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integrals". http://arxiv.org/abs/math/9409227v1
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`\eta_j` coefficients, and representation of the Hurwitz zeta
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function", arXiv:0706.0343v1 http://arxiv.org/abs/0706.0343
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.. [Cohen] Cohen, A.M. (2007). Numerical Methods for Laplace Transform
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Inversion, Springer.
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Math. 5 (1996) 329-359.
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http://www.apmaths.uwo.ca/~djeffrey/Offprints/W-adv-cm.pdf
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Third Edition. Springer.
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transform: a survey and comparison of methods. *Journal of
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Computational Physics* 33:1-32,
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transforms: Comparison of three new methods on characteristic
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problems from applications. *ACM Transactions on Mathematical
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Software* 19(3):333-359, http://dx.doi.org/10.1145/155743.155788
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.. [Froberg] Carl-Erik Froberg, "On the prime zeta function", BIT 8 (1968),
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pp. 187-202.
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distribution in the Gaussian copula model: a comparison of
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methods. *Journal of Credit Risk* 2(4):33-66,
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10.21314/JCR.2006.057
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15, p. 318-334 (1973)
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rules", mathematics of computation 23, p. 221-230 (1969)
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http://numbers.computation.free.fr/Constants/Gamma/gamma.pdf
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.. [GradshteynRyzhik] I S Gradshteyn & I M Ryzhik, A Jeffrey & D Zwillinger
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(eds.), *Table of Integrals, Series and Products*,
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Seventh edition (2007), Elsevier
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algorithm and related topics", *Journal of Computational
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and Applied Mathematics*, Volume 122, Issue 1-2
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(October 2000)
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.. [Homeier] H.H.H. Homeier - "Scalar Levin-Type Sequence Transformations"
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arXiv:math/0005209
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.. [Hoog] de Hoog, F., J. Knight, A. Stokes (1982). An improved method for
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numerical inversion of Laplace transforms. *SIAM Journal of
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Scientific and Statistical Computing* 3:357-366,
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http://dx.doi.org/10.1137/0903022
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.. [Kresser] Numerical Methods for General and Structured Eigenvalue Problems
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.. [Kuhlman] Kuhlman, K.L., (2013). Review of Inverse Laplace Transform
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Algorithms for Laplace-Space Numerical Approaches,
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*Numerical Algorithms*, 63(2):339-355.
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http://dx.doi.org/10.1007/s11075-012-9625-3
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.. [Lune84] J. van de Lune, 'Sums of Equal Powers of Positive Integers',
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Dissertation, Vrije Universiteit te Amsterdam, Centrum voor
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Wiskunde en Informatica, Amsterdam, 1984.
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.. [Lune86] J. van de Lune, H. J. J. te Riele, 'On the Zeros of the Riemann
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Zeta Function in the Critical Strip. III', Math. Comp. 41
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(1983) 759--767.
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.. [MPFR] The MPFR team. "The MPFR Library: Algorithms and Proofs",
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http://www.mpfr.org/algorithms.pdf
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.. [Michel] N. Michel, "Precise Coulomb wave functions for a wide
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range of complex `l`, `\eta` and `z`",
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http://arxiv.org/abs/physics/0702051v1
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Methods".
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Cambridge University Press, 1966
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functions", SIAM J. Numer. Anal. Vol. 31, No. 3, pp. 931-944,
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June 1994.
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Hypergeometric Series*. Ellis Horwood, 1985.
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.. [Stehfest] Stehfest, H. (1970). Algorithm 368: numerical inversion of
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of Complex Arguments and Order", J. Comp. Phys., vol 64, no.
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2, June 1986.
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Lecture Notes of the Unione Matematica Italiana, Springer, 2009.
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Acceleration of Convergence and the Summation of Divergent
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Series" arXiv:math/0306302
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4th Ed. 1946 Cambridge University Press
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http://functions.wolfram.com/
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