DLMF:19.2.E6 (Q6087)

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Language	Label	Description	Also known as
English	DLMF:19.2.E6	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle D\left(\phi,k\right)=\int_{0}^{\phi}\frac{{\sin^{% 2}}\theta\mathrm{d}\theta}{\sqrt{1-k^{2}{\sin^{2}}\theta}}=\int_{0}^{\sin\phi}% \frac{t^{2}\mathrm{d}t}{\sqrt{1-t^{2}}\sqrt{1-k^{2}t^{2}}}=(F\left(\phi,k% \right)-E\left(\phi,k\right))/k^{2}.}}

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DLMF:19.2.E6

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Symbols defined

incomplete elliptic integral of Legendre’s type

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Defining formula

{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

C1.S4.SS4.m1addec

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Legendre’s incomplete elliptic integral of the first kind

Defining formula

{\displaystyle{\displaystyle F\left(\NVar{\phi},\NVar{k}\right)}}

C19.S2.E4.m2aadec

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Legendre’s incomplete elliptic integral of the second kind

Defining formula

{\displaystyle{\displaystyle E\left(\NVar{\phi},\NVar{k}\right)}}

C19.S2.E5.m2aadec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3addec

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Defining formula

{\displaystyle{\displaystyle\sin\NVar{z}}}

C4.S14.E1.m2abdec

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Defining formula

{\displaystyle{\displaystyle\phi}}

C19.S1.XMD4.m1bdec

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Sitelinks

Wikipedia(0 entries)

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