DLMF:19.30.E6 (Q6680)

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Language	Label	Description	Also known as
English	DLMF:19.30.E6	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\frac{\partial s}{\partial(1/k)}=\sqrt{a^{2}-b^{2}% }F\left(\phi,k\right)=\sqrt{a^{2}-b^{2}}R_{F}\left(c-1,c-k^{2},c\right),}}

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DLMF:19.30.E6

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{\displaystyle{\displaystyle c={\csc^{2}}\phi}}

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{\displaystyle{\displaystyle k^{2}=(a^{2}-b^{2})/(a^{2}+\lambda)}}

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{\displaystyle{\displaystyle c={{\csc^{2}}}\phi}}

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symmetric elliptic integral of first kind

Defining formula

{\displaystyle{\displaystyle R_{F}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}

C19.S16.E1.m2aadec

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cosecant function

Defining formula

{\displaystyle{\displaystyle\csc\NVar{z}}}

C4.S14.E5.m2aadec

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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.m2adec

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partial derivative of $$f$$ with respect to $$x$$

Defining formula

{\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}

C1.S5.E3.m4adec

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partial differential of $$x$$

Defining formula

{\displaystyle{\displaystyle\partial\NVar{x}}}

C1.S5.E3.m2adec

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Defining formula

{\displaystyle{\displaystyle\phi}}

C19.S1.XMD4.m1ddec

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Defining formula

{\displaystyle{\displaystyle k}}

C19.S1.XMD5.m1ddec

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Sitelinks

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