explicit representations
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1: 18.5 Explicit Representations
2: 16.11 Asymptotic Expansions
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►Explicit representations for the coefficients are given in Volkmer (2023).
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►Explicit representations for the coefficients are given in Volkmer and Wood (2014).
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3: 26.13 Permutations: Cycle Notation
4: 18.20 Hahn Class: Explicit Representations
§18.20 Hahn Class: Explicit Representations
…5: 4.13 Lambert -Function
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►Explicit representations for the are given in Kalugin and Jeffrey (2011).
…See Jeffrey and Murdoch (2017) for an explicit representation for the in terms of associated Stirling numbers.
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6: Bibliography T
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Une nouvelle représentation explicite des nombres d’Euler.
C. R. Acad. Sci. Paris Sér. A-B 286 (19), pp. A807–A809.
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7: 18.37 Classical OP’s in Two or More Variables
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Explicit Representation
…8: 14.30 Spherical and Spheroidal Harmonics
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Explicit Representation
…9: 18.35 Pollaczek Polynomials
10: Errata
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Section 16.11(i)
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Expansion
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§4.13 has been enlarged. The Lambert -function is multi-valued and we use the notation , , for the branches. The original two solutions are identified via and .
Other changes are the introduction of the Wright -function and tree -function in (4.13.1_2) and (4.13.1_3), simplification formulas (4.13.3_1) and (4.13.3_2), explicit representation (4.13.4_1) for , additional Maclaurin series (4.13.5_1) and (4.13.5_2), an explicit expansion about the branch point at in (4.13.9_1), extending the number of terms in asymptotic expansions (4.13.10) and (4.13.11), and including several integrals and integral representations for Lambert -functions in the end of the section.