DLMF:19.9.E13

MaRDI QIDQ6952

• Label: DLMF:19.9.E13

Digital Library of Mathematical Functions ID 19.9.E13

${\displaystyle{\displaystyle\Pi\left(\phi,\alpha^{2},0\right)\leq\Pi\left(\phi,\alpha^{2},k\right)\leq\min(\Pi\left(\phi,\alpha^{2},0\right)/\Delta,\Pi\left(\phi,\alpha^{2},1\right)).}}$

Symbols List

• ${\displaystyle{\displaystyle\Pi\left(\NVar{\phi},\NVar{\alpha}^{2},\NVar{k}\right)}}$: Legendre’s incomplete elliptic integral of the third kind
• ${\displaystyle{\displaystyle\phi}}$: real or complex argument
• ${\displaystyle{\displaystyle k}}$: real or complex modulus
• ${\displaystyle{\displaystyle\alpha^{2}}}$: real or complex parameter
• ${\displaystyle{\displaystyle\Delta}}$: Δ
 

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