DLMF:12.2.E6 (Q4091)

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DLMF:12.2.E6
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    Statements

    Defining formula
    U ⁡ ( a , 0 ) = π 2 1 2 ⁢ a + 1 4 ⁢ Γ ⁡ ( 3 4 + 1 2 ⁢ a ) , parabolic-U 𝑎 0 𝜋 superscript 2 1 2 𝑎 1 4 Euler-Gamma 3 4 1 2 𝑎 {\displaystyle{\displaystyle U\left(a,0\right)=\frac{\sqrt{\pi}}{2^{\frac{1}{2% }a+\frac{1}{4}}\Gamma\left(\frac{3}{4}+\frac{1}{2}a\right)},}}
    0 references
    DLMF id
    DLMF:12.2.E6
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    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    Q11320
    Defining formula
    U ⁡ ( a , z ) parabolic-U 𝑎 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C12.S2.SS1.p1.m1aadec
    0 references
    Q11516
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C12.S1.XMD6.m1dec
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