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2: 28.18 Integrals and Integral Equations

… ►See §28.28.

3: 22.22 Software

… ►For other software see the Software Index. ►For another listing of Web-accessible software for the functions in this chapter, see GAMS (class C13). … ►See Bulirsch (1965b). Also see the Software Index. … ►See the Software Index.

4: 32.17 Methods of Computation

… ►The Painlevé equations can be integrated by Runge–Kutta methods for ordinary differential equations; see §3.7(v), Hairer et al. (2000), and Butcher (2003). For numerical studies of ${\text{P}}_{\text{I}}$ see Holmes and Spence (1984), Noonburg (1995), and Fornberg and Weideman (2011). For numerical studies of ${\text{P}}_{\text{II}}$ see Rosales (1978), Miles (1978, 1980), Kashevarov (1998, 2004), and S. …For numerical studies of ${\text{P}}_{\text{IV}}$ see Bassom et al. (1993).

5: 34.13 Methods of Computation

… ►Methods of computation for $\mathit{3}j$ and $\mathit{6}j$ symbols include recursion relations, see Schulten and Gordon (1975a), Luscombe and Luban (1998), and Edmonds (1974, pp. 42–45, 48–51, 97–99); summation of single-sum expressions for these symbols, see Varshalovich et al. (1988, §§8.2.6, 9.2.1) and Fang and Shriner (1992); evaluation of the generalized hypergeometric functions of unit argument that represent these symbols, see Srinivasa Rao and Venkatesh (1978) and Srinivasa Rao (1981). ►For $\mathit{9}j$ symbols, methods include evaluation of the single-sum series (34.6.2), see Fang and Shriner (1992); evaluation of triple-sum series, see Varshalovich et al. (1988, §10.2.1) and Srinivasa Rao et al. (1989). …See also Roothaan and Lai (1997) and references given there.

6: 3.12 Mathematical Constants

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3.12.3 $$\mathrm{e}=\mathrm{2.71828\hspace{0.33em}18284\hspace{0.33em}59045\hspace{0.33em}23536}\mathrm{\dots },$$

ⓘ

Symbols:

$\mathrm{e}$: base of natural logarithm

Notes:

For more digits see OEIS Sequence A001113; see also Sloane (2003).

Permalink:

http://dlmf.nist.gov/3.12.E3

Encodings:

pMML, png, TeX

See also:

Annotations for §3.12 and Ch.3

►see §4.2(ii), and Euler’s constant $\gamma$ …see §5.2(ii). ►For access to online high-precision numerical values of mathematical constants see Sloane (2003). For historical and other information see Finch (2003).

7: 20.16 Software

… ►For other software see the Software Index. … ►See the Software Index. … ►See the Software Index.

8: 32.16 Physical Applications

… ►For a survey see McCoy (1992). See also McCoy et al. (1977), Jimbo et al. (1980), Essler et al. (1996), and Kanzieper (2002). … ►See Bountis et al. (1982) and Grammaticos et al. (1991). … ►For applications in 2D quantum gravity and related aspects of the enumerative topology see Di Francesco et al. (1995). For applications in string theory see Seiberg and Shih (2005).

9: 4.11 Sums

… ►For infinite series involving logarithms and/or exponentials, see Gradshteyn and Ryzhik (2000, Chapter 1), Hansen (1975, §44), and Prudnikov et al. (1986a, Chapter 5).

10: 4.27 Sums

… ►For sums of trigonometric and inverse trigonometric functions see Gradshteyn and Ryzhik (2000, Chapter 1), Hansen (1975, §§14–42), Oberhettinger (1973), and Prudnikov et al. (1986a, Chapter 5).