Complete and incomplete elliptic integrals of the third kind
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ellipticPi(n,m) represents the complete elliptic
integral of the third kind
ellipticPi(n,φ,m) represents the incomplete
elliptic integral of the third kind
The elliptic integrals of the third kind are defined for complex arguments m, ϕ, and n.
If all arguments are numerical and at least one is a floating-point
floating-point results. For most exact arguments, it returns unevaluated
symbolic calls. You can approximate such results with floating-point
numbers using the
When called with floating-point 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 floating-point numbers, use
ellipticPi(PI/4, I); float(ellipticPi(PI/4, I))
Alternatively, use a floating-point value as an argument:
ellipticPi(1/2, 1, 1/4); ellipticPi(0.5, 1, 1/4)
Some special arguments return explicit symbolic representations:
ellipticPi(n, 0); ellipticPi(0, m); ellipticPi(0, p, m); ellipticPi(1, p, m)
An arithmetical expression specifying the parameter.
An arithmetical expression specifying the amplitude. The default is .
An arithmetical expression specifying the characteristic.