DLMF:5.10.E1 (Q2109)

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DLMF:5.10.E1
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    Statements

    Defining formula
    Ln ⁡ Γ ⁡ ( z ) + z - ( z - 1 2 ) ⁢ ln ⁡ z - 1 2 ⁢ ln ⁡ ( 2 ⁢ π ) = a 0 z + a 1 z + a 2 z + a 3 z + a 4 z + a 5 z + ⁢ ⋯ , multivalued-natural-logarithm Euler-Gamma 𝑧 𝑧 𝑧 1 2 𝑧 1 2 2 𝜋 continued-fraction subscript 𝑎 0 𝑧 continued-fraction subscript 𝑎 1 𝑧 continued-fraction subscript 𝑎 2 𝑧 continued-fraction subscript 𝑎 3 𝑧 continued-fraction subscript 𝑎 4 𝑧 continued-fraction subscript 𝑎 5 limit-from 𝑧 ⋯ {\displaystyle{\displaystyle\operatorname{Ln}\Gamma\left(z\right)+z-\left(z-% \tfrac{1}{2}\right)\ln z-\tfrac{1}{2}\ln\left(2\pi\right)=\cfrac{a_{0}}{z+% \cfrac{a_{1}}{z+\cfrac{a_{2}}{z+\cfrac{a_{3}}{z+\cfrac{a_{4}}{z+\cfrac{a_{5}}{% z+}}}}}}\cdots,}}
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    DLMF id
    DLMF:5.10.E1
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