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19 Elliptic IntegralsLegendre’s Integrals19.3 Graphics

Figure 19.3.5 (See in context.)

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Figure 19.3.5: Π(α2,k) as a function of k2 and α2 for -2k2<1, -2α22. Cauchy principal values are shown when α2>1. The function is unbounded as α21-, and also (with the same sign as 1-α2) as k21-. As α21+ it has the limit K(k)-(E(k)/k2). If α2=0, then it reduces to K(k). If k2=0, then it has the value 12π/1-α2 when α2<1, and 0 when α2>1. See §19.6(i). Magnify 3D Help