DLMF:13.3.E15 (Q4349)

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DLMF:13.3.E15
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    Statements

    Defining formula
    d d z ⁡ M ⁡ ( a , b , z ) = a b ⁢ M ⁡ ( a + 1 , b + 1 , z ) , derivative 𝑧 Kummer-confluent-hypergeometric-M 𝑎 𝑏 𝑧 𝑎 𝑏 Kummer-confluent-hypergeometric-M 𝑎 1 𝑏 1 𝑧 {\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}z}M\left(a,b,z\right)=% \frac{a}{b}M\left(a+1,b+1,z\right),}}
    0 references
    DLMF id
    DLMF:13.3.E15
    0 references
    Symbols used
    $$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ Kummer confluent hypergeometric function
    Defining formula
    M ⁡ ( a , b , z ) Kummer-confluent-hypergeometric-M 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle M\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
    xml-id
    C13.S2.E2.m2agdec
    0 references
     
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