DLMF:

19 Elliptic Integrals Legendre’s Integrals 19.3 Graphics 19.3 Graphics 19.4 Derivatives and Differential Equations

Figure 19.3.1 (See in context.)

Figure 19.3.1: $\mathop{K\/}\nolimits\!\left(k\right)$ and $\mathop{E\/}\nolimits\!\left(k\right)$ as functions of $k^{2}$ for $-2\leq k^{2}\leq 1$ . Graphs of $\mathop{{K^{{\prime}}}\/}\nolimits\!\left(k\right)$ and $\mathop{{E^{{\prime}}}\/}\nolimits\!\left(k\right)$ are the mirror images in the vertical line $k^{2}=\frac{1}{2}$ .

Annotations:

Symbols:: $\mathop{{K^{{\prime}}}\/}\nolimits\!\left(k\right)$ : Legendre’s complementary complete elliptic integral of the first kind, $\mathop{{E^{{\prime}}}\/}\nolimits\!\left(k\right)$ : Legendre’s complementary complete elliptic integral of the second kind, $\mathop{K\/}\nolimits\!\left(k\right)$ : Legendre’s complete elliptic integral of the first kind, $\mathop{E\/}\nolimits\!\left(k\right)$ : Legendre’s complete elliptic integral of the second kind and : real or complex modulus
Permalink:: http://dlmf.nist.gov/19.3.F1.mag
Encodings:: Magnified png, pdf

© 2010–2013 NIST / Privacy Policy / Disclaimer / Feedback; Version 1.0.6; Release date 2013-05-06 Math-Image version (See MathML) . A Printed Companionis available. 19.3 Graphics 19.4 Derivatives and Differential Equations