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1: 23.14 Integrals
2: 23.9 Laurent and Other Power Series
3: 11.14 Tables
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Abramowitz and Stegun (1964, Chapter 12) tabulates , , and for and , to 6D or 7D.
Agrest et al. (1982) tabulates and for and to 11D.
Barrett (1964) tabulates for and to 5 or 6S, to 2S.
Zhang and Jin (1996) tabulates and for and to 8D or 7S.
Agrest et al. (1982) tabulates and for to 11D.
4: 20 Theta Functions
Chapter 20 Theta Functions
…5: 18.39 Applications in the Physical Sciences
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βΊwhere is the (squared) angular momentum operator (14.30.12).
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βΊwith an infinite set of orthonormal eigenfunctions
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βΊis tridiagonalized in the complete non-orthogonal (with measure , ) basis of Laguerre functions:
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βΊFor either sign of , and chosen such that , , truncation of the basis to terms, with , the discrete eigenvectors are the orthonormal functions
…This equivalent quadrature relationship, see Heller et al. (1973), Yamani and Reinhardt (1975), allows extraction of scattering information from the finite dimensional functions of (18.39.53), provided that such information involves potentials, or projections onto functions, exactly expressed, or well approximated, in the finite basis of (18.39.44).
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6: 18.5 Explicit Representations
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βΊSimilarly in the cases of the ultraspherical polynomials and the Laguerre polynomials we assume that , and , unless
stated otherwise.
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7: 25.15 Dirichlet -functions
§25.15 Dirichlet -functions
βΊ§25.15(i) Definitions and Basic Properties
βΊThe notation was introduced by Dirichlet (1837) for the meromorphic continuation of the function defined by the series … … βΊ§25.15(ii) Zeros
…8: 25.12 Polylogarithms
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βΊOther notations and names for include (Kölbig et al. (1970)), Spence function (’t Hooft and Veltman (1979)), and (Maximon (2003)).
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9: 23.21 Physical Applications
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βΊIn §22.19(ii) it is noted that Jacobian elliptic functions provide a natural basis of solutions for problems in Newtonian classical dynamics with quartic potentials in canonical form .
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23.21.1
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23.21.3
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23.21.5
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