DLMF:13.2.E38 (Q4330)

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DLMF:13.2.E38
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    Statements

    test
    𝒲 ⁡ { U ⁡ ( a , b , z ) , e z ⁢ U ⁡ ( b - a , b , e ± π ⁢ i ⁢ z ) } = e ± ( a - b ) ⁢ π ⁢ i ⁢ z - b ⁢ e z . Wronskian Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 superscript 𝑒 𝑧 Kummer-confluent-hypergeometric-U 𝑏 𝑎 𝑏 superscript 𝑒 plus-or-minus 𝜋 imaginary-unit 𝑧 superscript 𝑒 plus-or-minus 𝑎 𝑏 𝜋 imaginary-unit superscript 𝑧 𝑏 superscript 𝑒 𝑧 {\displaystyle{\displaystyle\mathscr{W}\left\{U\left(a,b,z\right),e^{z}U\left(% b-a,b,e^{\pm\pi\mathrm{i}}z\right)\right\}=e^{\pm(a-b)\pi\mathrm{i}}z^{-b}e^{z% }.}}
    0 references
    DLMF id
    DLMF:13.2.E38
    0 references
    Symbols used
    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.m2avdec
    0 references
    Q10865
    test
    𝒲 Wronskian {\displaystyle{\displaystyle\mathscr{W}}}
    xml-id
    C1.S13.Px2.p1.m3aedec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ahdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aidec
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    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aedec
    0 references
    Q11557
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1akdec
    0 references
     
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