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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

Calling Sequence

EllipticPi(z, nu, k)

EllipticPi(nu, k)

EllipticCPi(nu, k)

Parameters

z

-

algebraic expression (the sine of the amplitude)

nu

-

algebraic expression (the characteristic)

k

-

algebraic expression (the parameter)

Description

• 

The incomplete elliptic integral EllipticPi is defined by

EllipticPiz,ν,k=0z11νt21t21k2t2ⅆt

• 

The complete elliptic integrals EllipticPi and EllipticCPi are defined by

EllipticPiν,k=EllipticPi1,ν,k

EllipticCPiν,k=EllipticPi1,ν,1k2

Examples

EllipticPi0.1,0.2,0.3

0.1002494388

(1)

EllipticPi0.2,0.3

1.800217337

(2)

EllipticCPi0.2,0.3

3.032020785

(3)

References

  

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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