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21—30 of 170 matching pages
21: 33.24 Tables
22: 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.
23: 10.25 Definitions
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§10.25(iii) Numerically Satisfactory Pairs of Solutions
►Table 10.25.1 lists numerically satisfactory pairs of solutions (§2.7(iv)) of (10.25.1). … ►24: Bibliography L
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Algorithm 917: complex double-precision evaluation of the Wright function.
ACM Trans. Math. Software 38 (3), pp. Art. 20, 17.
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An asymptotic estimate for the Bernoulli and Euler numbers.
Canad. Math. Bull. 20 (1), pp. 109–111.
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Comparison of a pair of upper bounds for a ratio of gamma functions.
Math. Balkanica (N.S.) 16 (1-4), pp. 195–202.
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25: 27.5 Inversion Formulas
26: 27.19 Methods of Computation: Factorization
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►Type II probabilistic algorithms for factoring rely on finding a pseudo-random pair of integers that satisfy .
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27: 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.
28: Peter L. Walker
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29: 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
30: 15.10 Hypergeometric Differential Equation
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►It has regular singularities at , with corresponding exponent pairs
, , , respectively.
When none of the exponent pairs differ by an integer, that is, when none of , , is an integer, we have the following pairs
, of fundamental solutions.
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►The three pairs of fundamental solutions given by (15.10.2), (15.10.4), and (15.10.6) can be transformed into 18 other solutions by means of (15.8.1), leading to a total of 24 solutions known as Kummer’s solutions.
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►The connection formulas for the principal branches of Kummer’s solutions are:
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