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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 Π(n|m)=Π(n|1m), where Π(n|m) is 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 value, 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 using the float function.

Environment Interactions

When called with floating-point arguments, this function is sensitive to the environment variable DIGITS which determines the numerical working precision.


Example 1

Most calls with exact arguments return themselves unevaluated. To approximate such values with floating-point numbers, use float:

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.

Return Values

Arithmetical expression.

See Also

MuPAD Functions

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