DLMF:19.5.E9 (Q6138)

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Language	Label	Description	Also known as
English	DLMF:19.5.E9	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle E\left(k\right)=K\left(k\right)+\frac{2\pi^{2}}{K% \left(k\right)}\,\frac{\sum_{n=1}^{\infty}(-1)^{n}n^{2}q^{n^{2}}}{1+2\sum_{n=1% }^{\infty}(-1)^{n}q^{n^{2}}},}}

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DLMF:19.5.E9

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{\displaystyle{\displaystyle|q|<1}}

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2afdec

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Defining formula

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

C19.S2.E8.m1acdec

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Defining formula

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

C19.S2.E8.m2aadec

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Defining formula

{\displaystyle{\displaystyle q}}

C22.S2.E1.m2acdec

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Defining formula

{\displaystyle{\displaystyle n}}

C19.S1.XMD3.m1bdec

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Defining formula

{\displaystyle{\displaystyle k}}

C19.S1.XMD5.m1gdec

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