DLMF:5.7.E3 (Q2079): Difference between revisions

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Property / constraint
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| z | < 2 𝑧 2 {\displaystyle{\displaystyle|z|<2}}

|z|<2
Property / constraint: | z | < 2 𝑧 2 {\displaystyle{\displaystyle|z|<2}} / rank
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Normal rank

Revision as of 16:04, 30 December 2019

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DLMF:5.7.E3
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    Statements

    ln ⁑ Ξ“ ⁑ ( 1 + z ) = - ln ⁑ ( 1 + z ) + z ⁒ ( 1 - Ξ³ ) + βˆ‘ k = 2 ∞ ( - 1 ) k ⁒ ( ΞΆ ⁑ ( k ) - 1 ) ⁒ z k k , Euler-Gamma 1 𝑧 1 𝑧 𝑧 1 superscript subscript π‘˜ 2 superscript 1 π‘˜ Riemann-zeta π‘˜ 1 superscript 𝑧 π‘˜ π‘˜ {\displaystyle{\displaystyle\ln\Gamma\left(1+z\right)=-\ln\left(1+z\right)+z(1% -\gamma)+\sum_{k=2}^{\infty}(-1)^{k}(\zeta\left(k\right)-1)\frac{z^{k}}{k},}}
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    | z | < 2 𝑧 2 {\displaystyle{\displaystyle|z|<2}}
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