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19 Elliptic IntegralsLegendre’s Integrals19.3 Graphics
Figure 19.3.5 (See in context.) 3D Help
See accompanying text
Figure 19.3.5: Π⁡(α2,k) as a function of k2 and α2 for −2≤k2<1, −2≤α2≤2. Cauchy principal values are shown when α2>1. The function is unbounded as α2→1−, and also (with the same sign as 1−α2) as k2→1−. As α2→1+ it has the limit K⁡(k)−(E⁡(k)/k′2). If α2=0, then it reduces to K⁡(k). If k2=0, then it has the value 12⁢π/1−α2 when α2<1, and 0 when α2>1. See §19.6(i). 3D Help
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