on%20finite%20point%20sets
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11: 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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12: 33.24 Tables
13: William P. Reinhardt
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►Reinhardt firmly believes that the Mandelbrot set is a special function, and notes with interest that the natural boundaries of analyticity of many “more normal” special functions are also fractals.
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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.
14: 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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15: 36.5 Stokes Sets
§36.5 Stokes Sets
… ►Stokes sets are surfaces (codimension one) in space, across which or acquires an exponentially-small asymptotic contribution (in ), associated with a complex critical point of or . …where denotes a real critical point (36.4.1) or (36.4.2), and denotes a critical point with complex or , connected with by a steepest-descent path (that is, a path where ) in complex or space. … ►Red and blue numbers in each region correspond, respectively, to the numbers of real and complex critical points that contribute to the asymptotics of the canonical integral away from the bifurcation sets. …The distribution of real and complex critical points in Figures 36.5.5 and 36.5.6 follows from consistency with Figure 36.5.1 and the fact that there are four real saddles in the inner regions. …16: 6.19 Tables
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Zhang and Jin (1996, pp. 652, 689) includes , , , 8D; , , , 8S.
Abramowitz and Stegun (1964, Chapter 5) includes the real and imaginary parts of , , , 6D; , , , 6D; , , , 6D.
Zhang and Jin (1996, pp. 690–692) includes the real and imaginary parts of , , , 8S.
17: Peter L. Walker
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18: Staff
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William P. Reinhardt, University of Washington, Chaps. 20, 22, 23
Peter L. Walker, American University of Sharjah, Chaps. 20, 22, 23
William P. Reinhardt, University of Washington, for Chaps. 20, 22, 23
Peter L. Walker, American University of Sharjah, for Chaps. 20, 22, 23
19: 25.12 Polylogarithms
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25.12.2
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►In the complex plane has a branch point at .
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►Sometimes the factor is omitted.
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20: 26.12 Plane Partitions
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►A plane partition, , of a positive integer , is a partition of in which the parts have been arranged in a 2-dimensional array that is weakly decreasing (nonincreasing) across rows and down columns.
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►An equivalent definition is that a plane partition is a finite subset of with the property that if and , then must be an element of .
…It is useful to be able to visualize a plane partition as a pile of blocks, one block at each lattice point
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26.12.26
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