Book:Murray R. Spiegel/Mathematical Handbook of Formulas and Tables/Chapter 34
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Murray R. Spiegel: Mathematical Handbook of Formulas and Tables: Chapter 34
Published $\text {1968}$
$34 \quad$ 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 First Kind
Incomplete Elliptic Integral of the Second Kind
Complete Elliptic Integral of the Second Kind
Incomplete Elliptic Integral of the Third Kind
Complete Elliptic Integral of the Third Kind
Landen's Transformation
Jacobi's Elliptic Functions
Addition Formulas
Derivatives
Series Expansions
Catalan's Constant
Periods of Elliptic Functions
Identities Involving Elliptic Functions
Special Values
Integrals
Legendre's Relation
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