Euler%20constant
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1—10 of 21 matching pages
1: 5.22 Tables
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►Abramowitz and Stegun (1964, Chapter 6) tabulates , , , and for to 10D; and for to 10D; , , , , , , , and for to 8–11S; for to 20S.
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2: 15.10 Hypergeometric Differential Equation
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►The connection formulas for the principal branches of Kummer’s solutions are:
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15.10.17
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15.10.18
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15.10.21
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15.10.25
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3: 5.11 Asymptotic Expansions
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►The scaled gamma function is defined in (5.11.3) and its main property is as in the sector .
Wrench (1968) gives exact values of up to .
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►In this subsection , , and are real or complex constants.
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5.11.12
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5.11.19
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4: 8.26 Tables
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Khamis (1965) tabulates for , to 10D.
Zhang and Jin (1996, Table 3.8) tabulates for , to 8D or 8S.
Abramowitz and Stegun (1964, pp. 245–248) tabulates for , to 7D; also for , to 6S.
Pagurova (1961) tabulates for , to 4-9S; for , to 7D; for , to 7S or 7D.
Zhang and Jin (1996, Table 19.1) tabulates for , to 7D or 8S.
5: 20.10 Integrals
6: 25.5 Integral Representations
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25.5.1
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25.5.13
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►In (25.5.15)–(25.5.19), , is the digamma function, and is Euler’s constant (§5.2).
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25.5.17
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25.5.19
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7: Bibliography
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Exact linearization of a Painlevé transcendent.
Phys. Rev. Lett. 38 (20), pp. 1103–1106.
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Tables of for Complex Argument.
Pergamon Press, New York.
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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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Repeated integrals and derivatives of Bessel functions.
SIAM J. Math. Anal. 20 (1), pp. 169–175.
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Numerical Tables for Angular Correlation Computations in -, - and -Spectroscopy: -, -, -Symbols, F- and -Coefficients.
Landolt-Börnstein Numerical Data and Functional Relationships
in Science and Technology, Springer-Verlag.
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8: 25.20 Approximations
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Cody et al. (1971) gives rational approximations for in the form of quotients of polynomials or quotients of Chebyshev series. The ranges covered are , , , . Precision is varied, with a maximum of 20S.
9: 30.9 Asymptotic Approximations and Expansions
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