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19 Elliptic IntegralsLegendre’s Integrals19.3 Graphics
Figure 19.3.2 (See in context.)
See accompanying text
Figure 19.3.2: R_{C}\left(x,1\right) and the Cauchy principal value of R_{C}\left(x,-1\right) for 0\leq x\leq 5. Both functions are asymptotic to \ln\left(4x\right)/\sqrt{4x} as x\to\infty; see (19.2.19) and (19.2.20). Note that R_{C}\left(x,\pm y\right)=y^{-1/2}R_{C}\left(x/y,\pm 1\right), y>0.