DLMF:19.29.E7 (Q6629): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:19.29.E7	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{y}^{x}\frac{a_{\alpha}+b_{\alpha}t}{a_{% \delta}+b_{\delta}t}\frac{\mathrm{d}t}{s(t)}=\tfrac{2}{3}d_{\alpha\beta}d_{% \alpha\gamma}R_{D}\left(U_{\alpha\beta}^{2},U_{\alpha\gamma}^{2},U_{\alpha% \delta}^{2}\right)+\frac{2X_{\alpha}Y_{\alpha}}{X_{\delta}Y_{\delta}U_{\alpha% \delta}},}}

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DLMF:19.29.E7

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{\displaystyle{\displaystyle U_{\alpha\delta}\neq 0}}

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elliptic integral symmetric in only two variables

Defining formula

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

C19.S16.E5.m2adec

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Defining formula

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

C1.S4.SS4.m1aadec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aadec

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Defining formula

{\displaystyle{\displaystyle X_{\alpha}}}

C19.S29.XMD1.m1cdec

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Defining formula

{\displaystyle{\displaystyle U_{n}}}

C19.S29.XMD10.m1cdec

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Defining formula

{\displaystyle{\displaystyle Y_{\alpha}}}

C19.S29.XMD2.m1cdec

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Defining formula

{\displaystyle{\displaystyle d_{\alpha\beta}}}

C19.S29.XMD3.m1bdec

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Defining formula

{\displaystyle{\displaystyle s(t)}}

C19.S29.XMD4.m1bdec

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