DLMF:13.2.E37 (Q4329)

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DLMF:13.2.E37
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    Statements

    test
    𝒲 ⁡ { z 1 - b ⁢ 𝐌 ⁡ ( a - b + 1 , 2 - b , z ) , e z ⁢ U ⁡ ( b - a , b , e ± π ⁢ i ⁢ z ) } = - z - b ⁢ e z / Γ ⁡ ( 1 - a ) , Wronskian superscript 𝑧 1 𝑏 Kummer-confluent-hypergeometric-bold-M 𝑎 𝑏 1 2 𝑏 𝑧 superscript 𝑒 𝑧 Kummer-confluent-hypergeometric-U 𝑏 𝑎 𝑏 superscript 𝑒 plus-or-minus 𝜋 imaginary-unit 𝑧 superscript 𝑧 𝑏 superscript 𝑒 𝑧 Euler-Gamma 1 𝑎 {\displaystyle{\displaystyle\mathscr{W}\left\{z^{1-b}{\mathbf{M}}\left(a-b+1,2% -b,z\right),e^{z}U\left(b-a,b,e^{\pm\pi\mathrm{i}}z\right)\right\}=-\ifrac{z^{% -b}e^{z}}{\Gamma\left(1-a\right)},}}
    0 references
    DLMF id
    DLMF:13.2.E37
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2apdec
    0 references
    Kummer confluent hypergeometric function
    test
    U ⁡ ( a , b , z ) Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
    xml-id
    C13.S2.E6.m2audec
    0 references
     
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