Digital Library of Mathematical Functions
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19 Elliptic IntegralsLegendre’s Integrals19.3 Graphics

Figure 19.3.11 (See in context.)

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Figure 19.3.11: (E(k)) as a function of complex k2 for -2(k2)2, -2(k2)2. The real part is symmetric under reflection in the real axis. On the branch cut (k2>1) it has the value kE(1/k)+(k2/k)K(1/k), with limit 1 as k21+.