DLMF:25.8.E6 (Q7663): Difference between revisions

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imported>Admin
Property / constraint
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| z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}

|z|<1
Property / constraint: | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}} / rank
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Normal rank

Revision as of 17:15, 30 December 2019

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DLMF:25.8.E6
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    Statements

    βˆ‘ k = 0 ∞ ΞΆ ⁑ ( 2 ⁒ k ) ⁒ z 2 ⁒ k = - 1 2 ⁒ Ο€ ⁒ z ⁒ cot ⁑ ( Ο€ ⁒ z ) , superscript subscript π‘˜ 0 Riemann-zeta 2 π‘˜ superscript 𝑧 2 π‘˜ 1 2 πœ‹ 𝑧 πœ‹ 𝑧 {\displaystyle{\displaystyle\sum_{k=0}^{\infty}\zeta\left(2k\right)z^{2k}=-% \tfrac{1}{2}\pi z\cot\left(\pi z\right),}}
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    | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}
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