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21—30 of 248 matching pages
21: 36 Integrals with Coalescing Saddles
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22: Gergő Nemes
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►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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23: Wolter Groenevelt
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►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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24: 22.6 Elementary Identities
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§22.6(ii) Double Argument
… ►§22.6(iii) Half Argument
… ►§22.6(iv) Rotation of Argument (Jacobi’s Imaginary Transformation)
…25: 33.24 Tables
26: 2.11 Remainder Terms; Stokes Phenomenon
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►However, on combining (2.11.6) with the connection formula (8.19.18), with , we derive
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►Following §2.4(iv), we rotate the integration path through an angle , which is valid by analytic continuation when .
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►For large , with (), the Whittaker function of the second kind has the asymptotic expansion (§13.19)
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►For example, using double precision is found to agree with (2.11.31) to 13D.
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27: 27.15 Chinese Remainder Theorem
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►Their product has 20 digits, twice the number of digits in the data.
…These numbers, in turn, are combined by the Chinese remainder theorem to obtain the final result , which is correct to 20 digits.
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28: William P. Reinhardt
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►In November 2015, Reinhardt was named Senior Associate Editor of the DLMF and Associate Editor for Chapters 20, 22, and 23.
29: 9.18 Tables
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Miller (1946) tabulates , for , for ; , for ; , for ; , , , (respectively , , , ) for . Precision is generally 8D; slightly less for some of the auxiliary functions. Extracts from these tables are included in Abramowitz and Stegun (1964, Chapter 10), together with some auxiliary functions for large arguments.
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.