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

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EllipticE - Incomplete and complete elliptic integrals of the second kind

EllipticCE - Complementary complete elliptic integral of the second kind

Calling Sequence

EllipticE(z,k)

EllipticE(k)

EllipticCE(k)

Parameters

z

-

algebraic expression (the sine of the amplitude)

k

-

algebraic expression (the parameter)

Description

• 

The incomplete elliptic integral EllipticE is defined by

EllipticEz,k=0zk2t2+1t2+1ⅆt

• 

The complete elliptic integrals EllipticE and EllipticCE are defined by

EllipticEk=EllipticE1,k

EllipticCEk=EllipticE1,k2+1

Examples

EllipticE0.2,0.3

0.2012363833

(1)

EllipticE0.3

1.534833465

(2)

EllipticCE0.3

1.096477517

(3)

See Also

EllipticCK, EllipticCPi, EllipticF, EllipticK, EllipticPi, JacobiSN, WeierstrassP

References

  

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


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