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DLMF:13.2.E36 - MaRDI portal

DLMF:13.2.E36 (Q5025)

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DLMF:13.2.E36
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    Statements

    DLMF defining formula
    𝒲 ⁑ { z 1 - b ⁒ 𝐌 ⁑ ( a - b + 1 , 2 - b , z ) , U ⁑ ( a , b , z ) } = - z - b ⁒ e z / Ξ“ ⁑ ( a - b + 1 ) , Wronskian superscript 𝑧 1 𝑏 Kummer-confluent-hypergeometric-bold-M π‘Ž 𝑏 1 2 𝑏 𝑧 Kummer-confluent-hypergeometric-U π‘Ž 𝑏 𝑧 superscript 𝑧 𝑏 superscript 𝑒 𝑧 Euler-Gamma π‘Ž 𝑏 1 {\displaystyle{\displaystyle\mathscr{W}\left\{z^{1-b}{\mathbf{M}}\left(a-b+1,2% -b,z\right),U\left(a,b,z\right)\right\}=-\ifrac{z^{-b}e^{z}}{\Gamma\left(a-b+1% \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.m2aodec
    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.m2atdec
    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.m2ahdec
    0 references
    Wronskian
    DLMF defining formula
    𝒲 Wronskian {\displaystyle{\displaystyle\mathscr{W}}}
    xml-id
    C1.S13.Px2.p1.m3acdec
    0 references
    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2agdec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1aidec
    0 references

    Identifiers

     
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