DLMF:10.43.E16 (Q3630)

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DLMF:10.43.E16
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    Statements

    test
    Ki α ⁡ ( 0 ) = π ⁢ Γ ⁡ ( 1 2 ⁢ α ) 2 ⁢ Γ ⁡ ( 1 2 ⁢ α + 1 2 ) , Bickley-Ki 𝛼 0 𝜋 Euler-Gamma 1 2 𝛼 2 Euler-Gamma 1 2 𝛼 1 2 {\displaystyle{\displaystyle\mathrm{Ki}_{\alpha}\left(0\right)=\frac{\sqrt{\pi% }\Gamma\left(\frac{1}{2}\alpha\right)}{2\Gamma\left(\frac{1}{2}\alpha+\frac{1}% {2}\right)},}}
    0 references
    DLMF id
    DLMF:10.43.E16
    0 references
    constraint
    α ≠ 0 , - 2 , - 4 , … 𝛼 0 2 4 … {\displaystyle{\displaystyle\alpha\neq 0,-2,-4,\dots}}
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    Symbols used
    Bickley function
    test
    Ki α ⁡ ( x ) Bickley-Ki 𝛼 𝑥 {\displaystyle{\displaystyle\mathrm{Ki}_{\NVar{\alpha}}\left(\NVar{x}\right)}}
    xml-id
    C10.S43.E11.m2aedec
    0 references
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2addec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
     
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