The second singular value 
, corresponding to
 |
(1)
|
is given by
 |  |  |
(2)
|
 |  |  |
(3)
|
 |  |  |
(4)
|
For this modulus,
![E(sqrt(2)-1)=1/4sqrt(pi/4)[(Gamma(1/8))/(Gamma(5/8))+(Gamma(5/8))/(Gamma(9/8))].](/images/equations/EllipticIntegralSingularValuek2/NumberedEquation2.svg) |
(5)
|
Elliptic Integral Singular Value--k_2
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Cite this as:
Weisstein, Eric W. "Elliptic Integral Singular Value--k_2." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/EllipticIntegralSingularValuek2.html