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DLMF: Figure 19.17.8 ‣ §19.17 Graphics ‣ Symmetric Integrals ‣ Chapter 19 Elliptic Integrals
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19 Elliptic IntegralsSymmetric Integrals19.17 Graphics
Figure 19.17.8 (See in context.) 3D Help
See accompanying text
Figure 19.17.8: RJ⁡(0,y,1,p), 0≤y≤1, −1≤p≤2. Cauchy principal values are shown when p<0. The function is asymptotic to 32⁢π/y⁢p as p→0+, and to (32/p)⁢ln⁡(16/y) as y→0+. As p→0− it has the limit (−6/y)⁢RG⁡(0,y,1). When p=1, it reduces to RD⁡(0,y,1). If y=1, then it has the value 32⁢π/(p+p) when p>0, and 32⁢π/(p−1) when p<0. See (19.20.10), (19.20.11), and (19.20.8) for the cases p→0±, y→0+, and y=1, respectively. 3D Help
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