3 Numerical Methods Areas 3.11 Approximation Techniques 4 Elementary Functions

§3.12 Mathematical Constants

ⓘ

Keywords:: mathematical constants
Permalink:: http://dlmf.nist.gov/3.12
See also:: Annotations for Ch.3

The fundamental constant

3.12.1		$\pi=3.14159\;26535\;89793\;23846\;\ldots$
ⓘ Defines: $\pi$ : the ratio of the circumference of a circle to its diameter Notes: For more digits see OEIS Sequence A000796; see also Sloane (2003). Permalink: http://dlmf.nist.gov/3.12.E1 Encodings: TeX, pMML, png See also: Annotations for §3.12 and Ch.3

can be defined analytically in numerous ways, for example,

3.12.2		$\pi=4\int_{0}^{1}\frac{\,\mathrm{d}t}{1+t^{2}}.$
ⓘ Symbols: $\pi$ : the ratio of the circumference of a circle to its diameter, $\,\mathrm{d}\NVar{x}$ : differential of $x$ and $\int$ : integral Permalink: http://dlmf.nist.gov/3.12.E2 Encodings: TeX, pMML, png See also: Annotations for §3.12 and Ch.3

Other constants that appear in the DLMF include the base $e$ of natural logarithms

3.12.3		$e=2.71828\;18284\;59045\;23536\;\ldots\,,$
ⓘ 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: TeX, pMML, png See also: Annotations for §3.12 and Ch.3

see §4.2(ii), and Euler’s constant $\gamma$

3.12.4		$\gamma=0.57721\;56649\;01532\;86060\;\ldots,$
ⓘ Symbols: $\gamma$ : Euler’s constant Notes: For more digits see OEIS Sequence A001620; see also Sloane (2003). Permalink: http://dlmf.nist.gov/3.12.E4 Encodings: TeX, pMML, png See also: Annotations for §3.12 and Ch.3

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).

3.11 Approximation Techniques 4 Elementary Functions

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