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19 Elliptic IntegralsLegendre’s Integrals19.3 Graphics

Figure 19.3.3 (See in context.)

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Figure 19.3.3: F(ϕ,k) as a function of k2 and sin2ϕ for -1k22, 0sin2ϕ1. If sin2ϕ=1 (k2), then the function reduces to K(k), becoming infinite when k2=1. If sin2ϕ=1/k2 (<1), then it has the value K(1/k)/k: put c=k2 in (19.25.5) and use (19.25.1).