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Digital Library of Mathematical Functions

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

Figure 19.17.6 (See in context.)

See accompanying text

Figure 19.17.6: Cauchy principal value of $\mathop{R_{J}\/}\nolimits\!\left(x,y,1,-0.5\right)$ for $0\leq x\leq 1$ , $y=0,\,0.1,\,0.5,\,1$ .

corresponds to $2(\mathop{R_{C}\/}\nolimits\!\left(x,-0.5\right)-\mathop{R_{C}\/}\nolimits\!% \left(x,1\right))$ .

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.F6.mag
Encodings:: Magnified png, pdf

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