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21: Gergő Nemes
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►Nemes has research interests in asymptotic analysis, Écalle theory, exact WKB analysis, and special functions.
►As of September 20, 2021, Nemes performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 25 Zeta and Related Functions.
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22: Wolter Groenevelt
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►Groenevelt’s research interests is in special functions and orthogonal polynomials and their relations with representation theory and interacting particle systems.
►As of September 20, 2022, Groenevelt performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 18 Orthogonal Polynomials.
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23: 9.18 Tables
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►Additional listings of early tables of the functions treated in this chapter are given in Fletcher et al. (1962) and Lebedev and Fedorova (1960).
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Zhang and Jin (1996, p. 337) tabulates , , , for to 8S and for to 9D.
Sherry (1959) tabulates , , , , ; 20S.
Zhang and Jin (1996, p. 339) tabulates , , , , , , , , ; 8D.
24: 26.11 Integer Partitions: Compositions
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denotes the number of compositions of , and is the number of compositions into exactly
parts.
is the number of compositions of with no 1’s, where again .
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26.11.1
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►The Fibonacci numbers are determined recursively by
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►Additional information on Fibonacci numbers can be found in Rosen et al. (2000, pp. 140–145).
25: DLMF Project News
error generating summary26: 26.6 Other Lattice Path Numbers
§26.6 Other Lattice Path Numbers
… ►Delannoy Number
… ►Motzkin Number
… ►Narayana Number
… ►§26.6(iv) Identities
…27: 26.14 Permutations: Order Notation
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►As an example, is an element of The inversion number is the number of pairs of elements for which the larger element precedes the smaller:
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►The Eulerian number, denoted , is the number of permutations in with exactly descents.
…The Eulerian number
is equal to the number of permutations in with exactly excedances.
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§26.14(iii) Identities
…28: Bibliography N
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The Development of Prime Number Theory: From Euclid to Hardy and Littlewood.
Springer-Verlag, Berlin.
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On an integral transform involving a class of Mathieu functions.
SIAM J. Math. Anal. 20 (6), pp. 1500–1513.
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Reduction and evaluation of elliptic integrals.
Math. Comp. 20 (94), pp. 223–231.
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A table of integrals of the error functions.
J. Res. Nat. Bur. Standards Sect B. 73B, pp. 1–20.
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29: Sidebar 7.SB1: Diffraction from a Straightedge
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►The faint circular patterns are additional diffraction effects due to imperfections in the edge.
30: 12 Parabolic Cylinder Functions
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