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21—30 of 30 matching pages
21: 6.16 Mathematical Applications
22: 25.12 Polylogarithms
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25.12.2
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►The principal branch has a cut along the interval
and agrees with (25.12.1) when ; see also §4.2(i).
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25.12.3
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23: 5.11 Asymptotic Expansions
24: 36.5 Stokes Sets
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►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.
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36.5.4
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36.5.7
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25: Bibliography I
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IEEE Standard for Interval Arithmetic: IEEE Std 1788-2015.
The Institute of Electrical and Electronics Engineers, Inc..
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IEEE Standard for Interval Arithmetic: IEEE Std 1788.1-2017.
The Institute of Electrical and Electronics Engineers, Inc..
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The real roots of Bernoulli polynomials.
Ann. Univ. Turku. Ser. A I 37, pp. 1–20.
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26: 18.39 Applications in the Physical Sciences
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►in which case the probability density is time-independent, as .
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►where the orthogonality measure is now ,
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►Orthogonality, with measure for , for fixed
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►normalized with measure , .
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►which maps onto .
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27: Bibliography
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Exact linearization of a Painlevé transcendent.
Phys. Rev. Lett. 38 (20), pp. 1103–1106.
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On the degrees of irreducible factors of higher order Bernoulli polynomials.
Acta Arith. 62 (4), pp. 329–342.
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Application of the combined nonlinear-condensation transformation to problems in statistical analysis and theoretical physics.
Comput. Phys. Comm. 150 (1), pp. 1–20.
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Introduction to Interval Computations.
Computer Science and Applied Mathematics, Academic Press Inc., New York.
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Repeated integrals and derivatives of Bessel functions.
SIAM J. Math. Anal. 20 (1), pp. 169–175.
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28: Errata
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Subsection 19.25(iii)
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Additions
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Table 3.5.21
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Chapters 8, 20, 36
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References
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The constraint was added to the first sentence of this section.
The correct corner coordinates for the 9-point square, given on the last line of this table, are . Originally they were given incorrectly as , .
Diagram | |||
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⋮ | |||
, | |||
Reported 2014-01-13 by Stanley Oleszczuk.
29: Bibliography C
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Calcolo delle funzioni speciali , , , , alle alte precisioni.
Atti Accad. Sci. Lett. Arti Palermo Ser. (5) 2(1981/82) (1), pp. 7–25 (Italian).
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Asymptotic estimates for generalized Stirling numbers.
Analysis (Munich) 20 (1), pp. 1–13.
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Validated computation of certain hypergeometric functions.
ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.
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Coulomb effects in the Klein-Gordon equation for pions.
Phys. Rev. C 20 (2), pp. 696–704.
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30: Bibliography F
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Sur certaines sommes des intégral-cosinus.
Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).
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Tables of Elliptic Integrals of the First, Second, and Third Kind.
Technical report
Technical Report ARL 64-232, Aerospace Research Laboratories, Wright-Patterson Air Force Base, Ohio.
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Tables of the line broadening function
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Monthly Notices Roy. Astronom. Soc. 129, pp. 221–235.
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On weighted polynomial approximation on the whole real axis.
Acta Math. Acad. Sci. Hungar. 20, pp. 223–225.
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