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11: 19.26 Addition Theorems
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►and two similar equations obtained by exchanging
with (and with ), or with (and with ).
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12: About the Project
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►The results have been published in book form as the NIST Handbook of Mathematical Functions, by Cambridge University Press, and disseminated in the free electronic Digital Library of Mathematical Functions.
These products resulted from the leadership of the Editors and Associate Editors pictured in Figure 1; the contributions of 29 authors, 10 validators, and 5 principal developers; and assistance from a large group of contributing developers, consultants, assistants and interns.
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►Since that time there have been a number of developments.
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13: 5.20 Physical Applications
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►In nonrelativistic quantum mechanics, collisions between two charged particles are described with the aid of the Coulomb phase shift ; see (33.2.10) and Clark (1979).
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►Suppose the potential energy of a gas of point charges with positions and free to move on the infinite line , is given by
…Then the partition function (with ) is given by
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5.20.3
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►For charges free to move on a circular wire of radius ,
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14: Bibliography S
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On an identity of Ramanujan based on the hypergeometric series
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J. Number Theory 69 (2), pp. 125–134.
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Staudt and arithmetical properties of Bernoulli numbers.
Historia Sci. (2) 5 (1), pp. 69–74.
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Numerical Methods Based on Sinc and Analytic Functions.
Springer Series in Computational Mathematics, Vol. 20, Springer-Verlag, New York.
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15: 16.10 Expansions in Series of Functions
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16.10.1
►Here , , and are free real or complex parameters.
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16.10.2
►When the series on the right-hand side converges in the half-plane .
►Expansions of the form are discussed in Miller (1997), and further series of generalized hypergeometric functions are given in Luke (1969b, Chapter 9), Luke (1975, §§5.10.2 and 5.11), and Prudnikov et al. (1990, §§5.3, 6.8–6.9).
16: Howard S. Cohl
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►In this regard, he has been exploring mathematical knowledge management and the digital expression of mostly unambiguous context-free full semantic information for mathematical formulae.
17: Bibliography F
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The Lamé wave equation.
Uspekhi Mat. Nauk 44 (1(265)), pp. 123–144, 248 (Russian).
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Faster computation of Bernoulli numbers.
J. Algorithms 13 (3), pp. 431–445.
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Portable Special Function Routines.
In Portability of Numerical Software (Oak Brook, Illinois, 1976), W. R. Cowell (Ed.),
Lecture Notes in Computer Science, Vol. 57, pp. 452–483.
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18: Bibliography E
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Generalized Bernoulli numbers, generalized irregular primes, and class number.
Ann. Univ. Turku. Ser. A I 178, pp. 1–72.
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Painlevé transcendent describes quantum correlation function of the antiferromagnet away from the free-fermion point.
J. Phys. A 29 (17), pp. 5619–5626.
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On the representations of a number as a sum of three squares.
Proc. London Math. Soc. (3) 9, pp. 575–594.
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Institutiones Calculi Integralis.
Opera Omnia (1), Vol. 11, pp. 110–113.
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Note on the -Laguerre orthogonal polynomials.
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19: 21.9 Integrable Equations
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21.9.2
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►These parameters, including , are not free: they are determined by a compact, connected Riemann surface (Krichever (1976)), or alternatively by an appropriate initial condition (Deconinck and Segur (1998)).
These solutions have been compared successfully with physical experiments for (Wiegel (1960), Hammack et al. (1989), and Hammack et al. (1995)).
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