# §3.12 Mathematical Constants

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 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 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 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 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).