Complementary complete elliptic integral of the third kind
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ellipticCPi(n,m) represents the complementary
complete elliptic integral of the third kind ,
the complete elliptic integral of the third kind:
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 floating-point
ellipticCPi(n,m) returns floating-point
results. For most exact arguments, it returns unevaluated symbolic
calls. You can approximate such results with floating-point numbers
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
ellipticCPi(-1, PI/4); float(ellipticCPi(-1, PI/4))
Alternatively, use floating-point values as arguments. If one argument is a floating-point value and the others can be converted to a floating-point values, then a floating-point 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.