DLMF:5.10.E1 (Q2109): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11285 / rank
 
Normal rank
Property / Symbols used: Q11285 / qualifier
 
Defining formula:

a k subscript 𝑎 𝑘 {\displaystyle{\displaystyle a_{k}}}

a_{k}
Property / Symbols used: Q11285 / qualifier
 
xml-id: C5.S10.XMD1.m1dec

Latest revision as of 19:39, 1 January 2020

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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,}}
    0 references
    DLMF id
    DLMF:5.10.E1
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    general logarithm function
    Defining formula
    Ln ⁡ z multivalued-natural-logarithm 𝑧 {\displaystyle{\displaystyle\operatorname{Ln}\NVar{z}}}
    xml-id
    C4.S2.E1.m2adec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
    0 references
    Q11273
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C5.S1.XMD7.m1dec
    0 references
    Q11285
    Defining formula
    a k subscript 𝑎 𝑘 {\displaystyle{\displaystyle a_{k}}}
    xml-id
    C5.S10.XMD1.m1dec
    0 references
     
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