Book:Murray R. Spiegel/Mathematical Handbook of Formulas and Tables/Chapter 34

Murray R. Spiegel: Mathematical Handbook of Formulas and Tables: Chapter 34

Published $1968$.

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$34 \quad$ Elliptic Functions

Incomplete Elliptic Integral of the First Kind

where $\phi = \operatorname {am} u$ is called the amplitude of $u$ and $x = \sin \phi$, where here and below $0 < k < 1$.

Complete Elliptic Integral of the Third Kind

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