DLMF:13.8.E14 (Q4439)

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DLMF:13.8.E14
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    Statements

    Defining formula
    U ⁡ ( - a , b , z ) ∼ ( z / a ) ( 1 - b ) / 2 ⁢ e z / 2 ⁢ Γ ⁡ ( 1 + a ) ⁢ ( C b - 1 ⁢ ( a , 2 ⁢ a ⁢ z ) ⁢ ∑ s = 0 ∞ p s ⁢ ( z ) ( - a ) s - z / a ⁢ C b ⁢ ( a , 2 ⁢ a ⁢ z ) ⁢ ∑ s = 0 ∞ q s ⁢ ( z ) ( - a ) s ) , asymptotic-expansion Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 superscript 𝑧 𝑎 1 𝑏 2 superscript 𝑒 𝑧 2 Euler-Gamma 1 𝑎 subscript 𝐶 𝑏 1 𝑎 2 𝑎 𝑧 superscript subscript 𝑠 0 subscript 𝑝 𝑠 𝑧 superscript 𝑎 𝑠 𝑧 𝑎 subscript 𝐶 𝑏 𝑎 2 𝑎 𝑧 superscript subscript 𝑠 0 subscript 𝑞 𝑠 𝑧 superscript 𝑎 𝑠 {\displaystyle{\displaystyle U\left(-a,b,z\right)\sim\left(z/a\right)^{(1-b)/2% }e^{z/2}\Gamma\left(1+a\right)\*\left(C_{b-1}(a,2\sqrt{az})\sum_{s=0}^{\infty}% \frac{p_{s}(z)}{(-a)^{s}}-\sqrt{z/a}C_{b}(a,2\sqrt{az})\sum_{s=0}^{\infty}% \frac{q_{s}(z)}{(-a)^{s}}\right),}}
    0 references
    DLMF id
    DLMF:13.8.E14
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aidec
    0 references
     
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