DLMF:12.2.E16 (Q4101)

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DLMF:12.2.E16
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    Statements

    Defining formula
    V ⁡ ( a , - z ) = cos ⁡ ( π ⁢ a ) Γ ⁡ ( 1 2 - a ) ⁢ U ⁡ ( a , z ) + sin ⁡ ( π ⁢ a ) ⁢ V ⁡ ( a , z ) . parabolic-V 𝑎 𝑧 𝜋 𝑎 Euler-Gamma 1 2 𝑎 parabolic-U 𝑎 𝑧 𝜋 𝑎 parabolic-V 𝑎 𝑧 {\displaystyle{\displaystyle V\left(a,-z\right)=\frac{\cos\left(\pi a\right)}{% \Gamma\left(\frac{1}{2}-a\right)}U\left(a,z\right)+\sin\left(\pi a\right)V% \left(a,z\right).}}
    0 references
    DLMF id
    DLMF:12.2.E16
    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.m2afdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ahdec
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    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.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.m1ahdec
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