Digital Library of Mathematical Functions
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19 Elliptic IntegralsSymmetric Integrals19.17 Graphics

Figure 19.17.8 (See in context.)

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Figure 19.17.8: RJ(0,y,1,p), 0y1, -1p2. Cauchy principal values are shown when p<0. The function is asymptotic to 32π/yp as p0+, and to (32/p)ln(16/y) as y0+. As p0- 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 32π/(p+p) when p>0, and 32π/(p-1) when p<0. See (19.20.10), (19.20.11), and (19.20.8) for the cases p0±, y0+, and y=1, respectively.