DLMF:

Digital Library of Mathematical Functions

About the Project

19 Elliptic Integrals Symmetric Integrals 19.17 Graphics 19.17 Graphics 19.18 Derivatives and Differential Equations

Figure 19.17.7 (See in context.)

See accompanying text

Figure 19.17.7: Cauchy principal value of $\mathop{R_{J}\/}\nolimits\!\left(0.5,y,1,p\right)$ for $y=0,\,0.01,\,0.05,\,0.2,\,1$ , $-1\leq p<0$ .

corresponds to $3(\mathop{R_{C}\/}\nolimits\!\left(0.5,p\right)-(\pi/\sqrt{8}))/(1-p)$ . As $p\to 0$ the curve for

has the finite limit $-8.10386\dots$ ; see (19.20.10).

Annotations:

Symbols:: $\mathop{R_{C}\/}\nolimits\!\left(x,y\right)$ : Carlson’s combination of inverse circular and inverse hyperbolic functions and $\mathop{R_{J}\/}\nolimits\!\left(x,y,z,p\right)$ : symmetric elliptic integral of third kind
Permalink:: http://dlmf.nist.gov/19.17.F7.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. 19.17 Graphics 19.18 Derivatives and Differential Equations