constants
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1: 3.12 Mathematical Constants
§3.12 Mathematical Constants
►The fundamental constant …Other constants that appear in the DLMF include the base of natural logarithms …see §4.2(ii), and Euler’s constant … ►For access to online high-precision numerical values of mathematical constants see Sloane (2003). …2: 30.1 Special Notation
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►The main functions treated in this chapter are the eigenvalues and the spheroidal wave functions , , , , and , .
…Meixner and Schäfke (1954) use , , , for , , , , respectively.
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►Flammer (1957) and Abramowitz and Stegun (1964) use for , for , and
…where is a normalization constant determined by
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real variable. Except in §§30.7(iv), 30.11(ii), 30.13, and 30.14, . | |
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arbitrary small positive constant. |
3: 16.15 Integral Representations and Integrals
4: 32.9 Other Elementary Solutions
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►with , , , and arbitrary constants.
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►with an arbitrary constant, which is solvable by quadrature.
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►with and arbitrary constants.
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►with an arbitrary constant, which is solvable by quadrature.
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►with and arbitrary constants.
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5: 5.17 Barnes’ -Function (Double Gamma Function)
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►Here is the Bernoulli number (§24.2(i)), and is Glaisher’s constant, given by
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5.17.6
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5.17.7
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►For Glaisher’s constant see also Greene and Knuth (1982, p. 100) and §2.10(i).
6: 30.5 Functions of the Second Kind
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►Other solutions of (30.2.1) with , , and are
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30.5.1
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30.5.2
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30.5.4
►with as in (30.11.4).
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7: 16.16 Transformations of Variables
8: 5.13 Integrals
9: 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.
Zhang and Jin (1996, pp. 67–69 and 72) tabulates , , , , , , , and for to 8D or 8S; for to 51S.
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►Abramov (1960) tabulates for () , () to 6D.
Abramowitz and Stegun (1964, Chapter 6) tabulates for () , () to 12D.
…Zhang and Jin (1996, pp. 70, 71, and 73) tabulates the real and imaginary parts of , , and for , to 8S.