Mathematical Constants

Mathematical Constants#

Degree#

property ctx.degree#

where ctx is math53, ctxboost or ctxflint.

Returns one degree of angle, \(1^{\circ} = \pi/180\). See also Wikipedia [1276], MathWorld [904], Mpmath [607], Mpmath [713], Mpmath [706].

In extended precision (32 bit version of xlcalcnet)

>>> from xlcalcnet import ereal
>>> ereal.ConstDegree()
ereal('1.7453292519943295769E-2')

In double precision (64 bit version of xlcalcnet)

>>> from xlcalcnet import ereal
>>> ereal.ConstDegree()
0.0174532925199433

Golden ratio phi#

property ctx.phi#

where ctx is math53, ctxboost or ctxflint.

Returns the golden ratio \(\phi = (1+\sqrt 5)/2\). See also Wikipedia [1283], MathWorld [907], Mpmath [614].

In extended precision (32 bit version of xlcalcnet)

>>> from xlcalcnet import ereal
>>> ereal.ConstPhi()
ereal('1.6180339887498948482')

In double precision (64 bit version of xlcalcnet)

>>> from xlcalcnet import ereal
>>> ereal.ConstPhi()
1.61803398874989

Natural logarithm of 2#

property ctx.ln2#

where ctx is math53, ctxboost or ctxflint.

Returns the logarithm of 2. See also Wikipedia [1267], MathWorld [912].

In extended precision (32 bit version of xlcalcnet)

>>> from xlcalcnet import ereal
>>> ereal.ConstLog2()
ereal('6.9314718055994530943E-1')

In double precision (64 bit version of xlcalcnet)

>>> from xlcalcnet import ereal
>>> ereal.ConstLog2()
0.693147180559945

Natural logarithm of 10#

property ctx.ln10#

where ctx is math53, ctxboost or ctxflint.

Returns the logarithm of 10. See also MathWorld [911].

In extended precision (32 bit version of xlcalcnet)

>>> from xlcalcnet import ereal
>>> ereal.ConstLog10()
ereal('2.3025850929940456840')

In double precision (64 bit version of xlcalcnet)

>>> from xlcalcnet import ereal
>>> ereal.ConstLog10()
2.30258509299405

Pi (\(\pi\))#

property ctx.pi#

where ctx is math53, ctxboost or ctxflint.

Returns the constant pi. See also Wikipedia [1268], MathWorld [913], Mpmath [619].

In extended precision (32 bit version of xlcalcnet)

>>> from xlcalcnet import ereal
>>> ereal.Pi()
ereal('3.1415926535897932385')

In double precision (64 bit version of xlcalcnet)

>>> from xlcalcnet import ereal
>>> ereal.Pi()
3.14159265358979

Euler e#

property ctx.e#

where ctx is math53, ctxboost or ctxflint.

Returns the constant const_e. See also Wikipedia [1272], MathWorld [914], Mpmath [604].

In extended precision (32 bit version of xlcalcnet)

>>> from xlcalcnet import ereal
>>> ereal.ConstE()
ereal('3.1415926535897932385')

In double precision (64 bit version of xlcalcnet)

>>> from xlcalcnet import ereal
>>> ereal.ConstE()
2.71828182845905

Euler-Mascheroni constant \(\gamma\)#

property ctx.egamma#

where ctx is math53, ctxboost or ctxflint.

Returns the Euler gamma constant. See also Wikipedia [1281], MathWorld [905], Mpmath [612].

In extended precision (32 bit version of xlcalcnet)

>>> from xlcalcnet import ereal
>>> ereal.ConstEulerGamma()
ereal('5.7721566490153286062E-1')

In double precision (64 bit version of xlcalcnet)

>>> from xlcalcnet import ereal
>>> ereal.ConstEulerGamma()
0.577215664901533

Apéry’s constant#

property ctx.apery#

where ctx is math53, ctxboost or ctxflint.

Represents Apery’s constant. See also Wikipedia [1273], MathWorld [899], Mpmath [602].

It is an irrational number approximately equal to 1.2020569 given by

\[\zeta(3) = \sum_{k=1}^\infty\frac{1}{k^3}.\]

In extended precision (32 bit version of xlcalcnet)

>>> from xlcalcnet import ereal
>>> ereal.ConstApery()
ereal('1.2020569031595942854')

In double precision (64 bit version of xlcalcnet)

>>> from xlcalcnet import ereal
>>> ereal.ConstApery()
1.20205690315959

Catalan’s constant#

property ctx.catalan#

where ctx is math53, ctxboost or ctxflint.

Returns the Catalan constant. See also Wikipedia [1284], MathWorld [900], Mpmath [606].

Catalan’s constant \(K\) = 0.91596559… is given by the infinite series

\[K = \sum_{k=0}^{\infty} \frac{(-1)^k}{(2k+1)^2}.\]

In extended precision (32 bit version of xlcalcnet)

>>> from xlcalcnet import ereal
>>> ereal.ConstCatalan()
ereal('9.1596559417721901505E-1')

In double precision (64 bit version of xlcalcnet)

>>> from xlcalcnet import ereal
>>> ereal.ConstCatalan()
0.915965594177219

Glaisher’s constant#

property ctx.glaisher#

where ctx is math53, ctxboost or ctxflint.

Returns Glaisher’s constant. See also Wikipedia [1282], MathWorld [906], Mpmath [613].

The constant is defined as \(A = \exp(1/12-\zeta'(-1))\) where \(\zeta'(s)\) denotes the derivative of the Riemann zeta function.

In extended precision (32 bit version of xlcalcnet)

>>> from xlcalcnet import ereal
>>> ereal.ConstGlaisher()
ereal('1.2824271291006226369')

In double precision (64 bit version of xlcalcnet)

>>> from xlcalcnet import ereal
>>> ereal.ConstGlaisher()
1.28242712910062

Khinchin’s constant#

property ctx.khinchin#

where ctx is math53, ctxboost or ctxflint.

Returns Khinchin’s constant. See also Wikipedia [1289], MathWorld [908], Mpmath [618].

In extended precision (32 bit version of xlcalcnet)

>>> from xlcalcnet import ereal
>>> ereal.ConstKhinchin()
ereal('2.6854520010653064454')

In double precision (64 bit version of xlcalcnet)

>>> from xlcalcnet import ereal
>>> ereal.ConstKhinchin()
2.68545200106531

Imaginary One#

property ctx.onej#

where ctx is math53, ctxboost or ctxflint.

Returns the imaginary unit.

In extended precision (32 bit version of xlcalcnet)

>>> from xlcalcnet import ereal
>>> ereal.ConstDegree()
ereal('1.7453292519943295769E-2')

In double precision (64 bit version of xlcalcnet)

>>> from xlcalcnet import ereal
>>> ereal.ConstDegree()
0.0174532925199433
Contents