DLMF:13.31.E3 (Q4678)

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DLMF:13.31.E3
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    Statements

    Defining formula
    z a ⁢ U ⁡ ( a , 1 + a - b , z ) = lim n → ∞ ⁡ A n ⁢ ( z ) B n ⁢ ( z ) . superscript 𝑧 𝑎 Kummer-confluent-hypergeometric-U 𝑎 1 𝑎 𝑏 𝑧 subscript → 𝑛 subscript 𝐴 𝑛 𝑧 subscript 𝐵 𝑛 𝑧 {\displaystyle{\displaystyle z^{a}U\left(a,1+a-b,z\right)=\lim_{n\to\infty}% \frac{A_{n}(z)}{B_{n}(z)}.}}
    0 references
    DLMF id
    DLMF:13.31.E3
    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.m2adec
    0 references
    Q11559
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C13.S1.XMD2.m1bdec
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    Q11557
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1bdec
    0 references
    expansion (locally)
    Defining formula
    A n ⁢ ( z ) subscript 𝐴 𝑛 𝑧 {\displaystyle{\displaystyle A_{n}(z)}}
    xml-id
    C13.S31.XMD1.m1adec
    0 references
    expansion (locally)
    Defining formula
    B n ⁢ ( z ) subscript 𝐵 𝑛 𝑧 {\displaystyle{\displaystyle B_{n}(z)}}
    xml-id
    C13.S31.XMD2.m1adec
    0 references
     
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