DLMF:12.2.E15 (Q4100)

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DLMF:12.2.E15
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    Statements

    Defining formula
    U ⁡ ( a , - z ) = - sin ⁡ ( π ⁢ a ) ⁢ U ⁡ ( a , z ) + π Γ ⁡ ( 1 2 + a ) ⁢ V ⁡ ( a , z ) , parabolic-U 𝑎 𝑧 𝜋 𝑎 parabolic-U 𝑎 𝑧 𝜋 Euler-Gamma 1 2 𝑎 parabolic-V 𝑎 𝑧 {\displaystyle{\displaystyle U\left(a,-z\right)=-\sin\left(\pi a\right)U\left(% a,z\right)+\frac{\pi}{\Gamma\left(\frac{1}{2}+a\right)}V\left(a,z\right),}}
    0 references
    DLMF id
    DLMF:12.2.E15
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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.m2aedec
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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.m2agdec
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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.m1agdec
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