DLMF:19.9.E16 (Q6259)

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Language	Label	Description	Also known as
English	DLMF:19.9.E16	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle F\left(\phi,k\right)=\frac{2}{\pi}K\left(k^{% \prime}\right)\ln\left(\frac{4}{\Delta+\cos\phi}\right)-\theta\Delta^{2},}}

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DLMF:19.9.E16

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{\displaystyle{\displaystyle(\sin\phi)/8<\theta<(\ln 2)/(k^{2}\sin\phi)}}

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2aedec

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Defining formula

{\displaystyle{\displaystyle K\left(\NVar{k}\right)}}

C19.S2.E8.m1agdec

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cosine function

Defining formula

{\displaystyle{\displaystyle\cos\NVar{z}}}

C4.S14.E2.m2abdec

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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.m2acdec

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principal branch of logarithm function

Defining formula

{\displaystyle{\displaystyle\ln\NVar{z}}}

C4.S2.E2.m2aedec

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Defining formula

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

C4.S14.E1.m2acdec

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Defining formula

{\displaystyle{\displaystyle\phi}}

C19.S1.XMD4.m1edec

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Defining formula

{\displaystyle{\displaystyle k}}

C19.S1.XMD5.m1ndec

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Defining formula

{\displaystyle{\displaystyle k^{\prime}}}

C19.S1.XMD6.m1hdec

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Defining formula

{\displaystyle{\displaystyle\Delta}}

C19.S9.XMD2.m1edec

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