Catalan constant
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1: 26.5 Lattice Paths: Catalan Numbers
§26.5 Lattice Paths: Catalan Numbers
►§26.5(i) Definitions
► is the Catalan number. … ►§26.5(ii) Generating Function
… ►§26.5(iii) Recurrence Relations
…2: 25.11 Hurwitz Zeta Function
3: 26.6 Other Lattice Path Numbers
4: 26.1 Special Notation
5: 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). …6: 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. |
7: 16.15 Integral Representations and Integrals
8: 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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9: 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).