DLMF:5.11.E1 (Q2117)

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DLMF:5.11.E1
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    Statements

    Defining formula
    Ln ⁡ Γ ⁡ ( z ) ∼ ( z - 1 2 ) ⁢ ln ⁡ z - z + 1 2 ⁢ ln ⁡ ( 2 ⁢ π ) + ∑ k = 1 ∞ B 2 ⁢ k 2 ⁢ k ⁢ ( 2 ⁢ k - 1 ) ⁢ z 2 ⁢ k - 1 asymptotic-expansion multivalued-natural-logarithm Euler-Gamma 𝑧 𝑧 1 2 𝑧 𝑧 1 2 2 𝜋 superscript subscript 𝑘 1 Bernoulli-number-B 2 𝑘 2 𝑘 2 𝑘 1 superscript 𝑧 2 𝑘 1 {\displaystyle{\displaystyle\operatorname{Ln}\Gamma\left(z\right)\sim\left(z-% \tfrac{1}{2}\right)\ln z-z+\tfrac{1}{2}\ln\left(2\pi\right)+\sum_{k=1}^{\infty% }\frac{B_{2k}}{2k(2k-1)z^{2k-1}}}}
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    DLMF id
    DLMF:5.11.E1
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