§3.12 Mathematical Constants

Keywords:: mathematical constants
Permalink:: http://dlmf.nist.gov/3.12

The fundamental constant

3.12.1 $\pi=3.14159\; 26535\; 89793\; 23846\;\ldots$

Notes:: For more digits see OEIS Sequence A000796; see also Sloane (2003).
Permalink:: http://dlmf.nist.gov/3.12.E1
Encodings:: TeX, pMML, png

can be defined analytically in numerous ways, for example,

3.12.2 $\pi=4\int _{0}^{1}\frac{dt}{1+t^{2}}.$

Symbols:: $dx$ : differential of $x$ and $\int$ : integral
Permalink:: http://dlmf.nist.gov/3.12.E2
Encodings:: TeX, pMML, png

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

3.12.3 $e=2.71828\; 18284\; 59045\; 23536\;\ldots\,,$

Notes:: For more digits see OEIS Sequence A001113; see also Sloane (2003).
Symbols:: $e$ : base of exponential function
Permalink:: http://dlmf.nist.gov/3.12.E3
Encodings:: TeX, pMML, png

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

3.12.4 $\EulerConstant=0.57721\; 56649\; 0 1532\; 86060\;\ldots,$

Notes:: For more digits see OEIS Sequence A001620; see also Sloane (2003).
Symbols:: $\EulerConstant$ : Euler’s constant
Permalink:: http://dlmf.nist.gov/3.12.E4
Encodings:: TeX, pMML, png

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).