DLMF:12.2.E9 (Q4094)

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DLMF:12.2.E9
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    Statements

    test
    V ′ ⁡ ( a , 0 ) = π ⁢ 2 1 2 ⁢ a + 3 4 ( Γ ⁡ ( 1 4 - 1 2 ⁢ a ) ) 2 ⁢ Γ ⁡ ( 3 4 + 1 2 ⁢ a ) . diffop parabolic-V 1 𝑎 0 𝜋 superscript 2 1 2 𝑎 3 4 superscript Euler-Gamma 1 4 1 2 𝑎 2 Euler-Gamma 3 4 1 2 𝑎 {\displaystyle{\displaystyle V'\left(a,0\right)=\frac{\pi 2^{\frac{1}{2}a+% \frac{3}{4}}}{\left(\Gamma\left(\frac{1}{4}-\frac{1}{2}a\right)\right)^{2}% \Gamma\left(\frac{3}{4}+\frac{1}{2}a\right)}.}}
    0 references
    DLMF id
    DLMF:12.2.E9
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    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2acdec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
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