EllipticPi
Incomplete and complete elliptic integrals of the third kind
EllipticCPi
Complementary complete elliptic integral of the third kind
Calling Sequence
Parameters
Description
Examples
References
EllipticPi(z, nu, k)
EllipticPi(nu, k)
EllipticCPi(nu, k)
z
-
algebraic expression (the sine of the amplitude)
nu
algebraic expression (the characteristic)
k
algebraic expression (the parameter)
The incomplete elliptic integral EllipticPi is defined by
EllipticPiz,ν,k=∫0z11−νt21−t21−k2t2ⅆt
The complete elliptic integrals EllipticPi and EllipticCPi are defined by
EllipticPiν,k=EllipticPi1,ν,k
EllipticCPiν,k=EllipticPi1,ν,1−k2
EllipticPi0.1,0.2,0.3
0.1002494388
EllipticPi0.2,0.3
1.800217337
EllipticCPi0.2,0.3
3.032020785
Abramowitz, M., and Stegun, I., eds. Handbook of Mathematical Functions. New York: Dover, 1972.
See Also
EllipticCE
EllipticCK
EllipticE
EllipticF
EllipticK
JacobiSN
WeierstrassP
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