DLMF: Figure 19.3.7 ‣ §19.3 Graphics ‣ Legendre’s Integrals ‣ Chapter 19 Elliptic Integrals

Figure 19.3.7 (See in context.)

Figure 19.3.7:

K\left(k\right)

as a function of complex

k^{2}

for

-2\leq\Re\left(k^{2}\right)\leq 2

-2\leq\Im\left(k^{2}\right)\leq 2

. There is a branch cut where

1<k^{2}<\infty

ⓘ

Symbols:: $K\left(\NVar{k}\right)$ : Legendre’s complete elliptic integral of the first kind, $\Im$ : imaginary part, $\Re$ : real part and $k$ : real or complex modulus
Permalink:: http://dlmf.nist.gov/19.3.F7.viz

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