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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

Parameters

Description

Examples

References

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)

References

  

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

See Also

EllipticCK

EllipticCPi

EllipticF

EllipticK

EllipticPi

JacobiSN

WeierstrassP

 


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