Incomplete and complete elliptic integrals of the third kind - Maple Help

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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

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)

See Also

EllipticCE, EllipticCK, EllipticE, EllipticF, EllipticK, JacobiSN, WeierstrassP

References

  

Abramowitz, M., and Stegun, I., eds. Handbook of Mathematical Functions. New York: Dover, 1972.


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