ddg.math.functions module

Basic functions and math expressions.

ddg.math.functions.qgamma(z, q)

A generalised variant of mpmath.qgamma().

Unlike mpmath.qgamma(), this function returns infinity instead of raising a ZeroDivisionError.

Parameters:

zcomplex or mpmath.mpf

qcomplex or mpmath.mpf

Returns:

mpmath.mpf or mpmath.mpc

If the result is complex, mpmath.mpc will be returned. Otherwise mpmath.mpf.

Examples

>>> from ddg.math.functions import qgamma
>>> qgamma(4, 0.75)
mpf('4.046875')
>>> qgamma(6, 6)
mpf('121226245.0')
>>> qgamma(3 + 4j, 0.5j)
mpc(real='0.16630823822551999', imag='0.019524745760259529')
>>> qgamma(0, 1)
mpf('+inf')

ddg.math.functions.double_factorial(n)

The double factorial function.

\[\begin{split}\text{double_factorial}(n) = \begin{cases} n \cdot \text{double_factorial}(n - 2) &\text{ if } n \ge 2 \\ 1 &\text{ otherwise}. \end{cases}\end{split}\]

Parameters:

nint

Returns:

int

Examples

>>> from ddg.math.functions import double_factorial
>>> double_factorial(4)
8
>>> double_factorial(10)
3840
>>> double_factorial(0)
1

ddg.math.functions.sn(u, k)

ddg.math.functions.cn(u, k)

ddg.math.functions.dn(u, k)

ddg.math.functions.ns(u, k)

ddg.math.functions.nc(u, k)

ddg.math.functions.nd(u, k)

ddg.math.functions.sc(u, k)

ddg.math.functions.sd(u, k)

ddg.math.functions.dc(u, k)

ddg.math.functions.ds(u, k)

ddg.math.functions.cs(u, k)

ddg.math.functions.cd(u, k)

ddg.math.functions.K(k)