Complementary complete elliptic integral of the third kind
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ellipticCPi(n
,m
)
ellipticCPi(n,m)
represents the complementary
complete elliptic integral of the third kind $${\Pi}^{\prime}\left(nm\right)=\Pi \left(n1m\right)$$,
where $$\Pi \left(nm\right)$$ is
the complete elliptic integral of the third kind:
$$\Pi \left(n,m\right)=\Pi \left(n;\text{\hspace{0.17em}}\frac{\pi}{2}m\right)={\displaystyle \underset{0}{\overset{\pi /2}{\int}}\frac{1}{\left(1n{\mathrm{sin}}^{2}\theta \right)\sqrt{1m{\mathrm{sin}}^{2}\theta}}d}\theta $$
The complementary complete elliptic integral of the third kind is defined for complex arguments m and n.
If all arguments are numerical and at least one is a floatingpoint
value, ellipticCPi(n,m)
returns floatingpoint
results. For most exact arguments, it returns unevaluated symbolic
calls. You can approximate such results with floatingpoint numbers
using the float
function.
When called with floatingpoint arguments, this function is
sensitive to the environment variable DIGITS
which determines
the numerical working precision.
Most calls with exact arguments return themselves unevaluated.
To approximate such values with floatingpoint numbers, use float
:
ellipticCPi(1, PI/4); float(ellipticCPi(1, PI/4))
Alternatively, use floatingpoint values as arguments. If one argument is a floatingpoint value and the others can be converted to a floatingpoint values, then a floatingpoint result will be returned:
ellipticCPi(1/2, 1/4); ellipticCPi(0.5, 1/4)
Some special arguments return explicit symbolic representations:
ellipticCPi(0, m); ellipticCPi(n, 1)

An arithmetical expression specifying the parameter. 

An arithmetical expression specifying the characteristic. 
Arithmetical expression.