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keisanHigh-precision calculations for everyday life and work

Complete elliptic integrals K(k), E(k) (graph)

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Calculate and graph the tables for the 1st-kind complete elliptic integral K(k) and the 2nd-kind complete elliptic integral E(k).
Initial value of k
-1≦k≦1
]
\(\normalsize Complete\ elliptic\ integrals\ of\\ \ the\ 1st\ kind\ K(k)\ and\ 2nd\ kind\ E(k)\\ (1)\ K(k)={\large\int_{\small 0}^{\small 1}\frac{dt}{\sqrt{(1-t^2)(1-k^2t^2)}}}\\ (2)\ E(k)={\large\int_{\small 0}^{\small 1}\sqrt{\frac{1-k^2t^2}{1-t^2}}}dt\\\)

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