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DLMF:13.2.E34 - MaRDI portal

DLMF:13.2.E34 (Q5023)

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DLMF:13.2.E34
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    Statements

    DLMF defining formula
    𝒲 ⁑ { 𝐌 ⁑ ( a , b , z ) , U ⁑ ( a , b , z ) } = - z - b ⁒ e z / Ξ“ ⁑ ( a ) , Wronskian Kummer-confluent-hypergeometric-bold-M π‘Ž 𝑏 𝑧 Kummer-confluent-hypergeometric-U π‘Ž 𝑏 𝑧 superscript 𝑧 𝑏 superscript 𝑒 𝑧 Euler-Gamma π‘Ž {\displaystyle{\displaystyle\mathscr{W}\left\{{\mathbf{M}}\left(a,b,z\right),U% \left(a,b,z\right)\right\}=-\ifrac{z^{-b}e^{z}}{\Gamma\left(a\right)},}}
    0 references
    Symbols used
    gamma function
    DLMF defining formula
    Ξ“ ⁑ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2amdec
    0 references
    Kummer confluent hypergeometric function
    DLMF defining formula
    U ⁑ ( a , b , z ) Kummer-confluent-hypergeometric-U π‘Ž 𝑏 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
    xml-id
    C13.S2.E6.m2ardec
    0 references
    Olver’s confluent hypergeometric function
    DLMF defining formula
    𝐌 ⁑ ( a , b , z ) Kummer-confluent-hypergeometric-bold-M π‘Ž 𝑏 𝑧 {\displaystyle{\displaystyle{\mathbf{M}}\left(\NVar{a},\NVar{b},\NVar{z}\right% )}}
    xml-id
    C13.S2.E3.m2afdec
    0 references
    Wronskian
    DLMF defining formula
    𝒲 Wronskian {\displaystyle{\displaystyle\mathscr{W}}}
    xml-id
    C1.S13.Px2.p1.m3aadec
    0 references
    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aedec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1agdec
    0 references

    Identifiers

     
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