DLMF:13.3.E25 (Q4359)

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DLMF:13.3.E25
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    Statements

    Defining formula
    d n d z n ⁡ ( z b - 1 ⁢ U ⁡ ( a , b , z ) ) = ( - 1 ) n ⁢ ( a - b + 1 ) n ⁢ z b - n - 1 ⁢ U ⁡ ( a , b - n , z ) , derivative 𝑧 𝑛 superscript 𝑧 𝑏 1 Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 superscript 1 𝑛 Pochhammer 𝑎 𝑏 1 𝑛 superscript 𝑧 𝑏 𝑛 1 Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑛 𝑧 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\left(z^% {b-1}U\left(a,b,z\right)\right)=(-1)^{n}{\left(a-b+1\right)_{n}}z^{b-n-1}U% \left(a,b-n,z\right),}}
    0 references
    DLMF id
    DLMF:13.3.E25
    0 references
    Symbols used
    Kummer confluent hypergeometric function
    Defining formula
    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.m2ajdec
    0 references
     
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