DLMF:13.19.E1 (Q4587)

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DLMF:13.19.E1
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    Statements

    Defining formula
    M κ , μ ⁡ ( x ) ∼ Γ ⁡ ( 1 + 2 ⁢ μ ) Γ ⁡ ( 1 2 + μ - κ ) ⁢ e 1 2 ⁢ x ⁢ x - κ ⁢ ∑ s = 0 ∞ ( 1 2 - μ + κ ) s ⁢ ( 1 2 + μ + κ ) s s ! ⁢ x - s , asymptotic-expansion Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑥 Euler-Gamma 1 2 𝜇 Euler-Gamma 1 2 𝜇 𝜅 superscript 𝑒 1 2 𝑥 superscript 𝑥 𝜅 superscript subscript 𝑠 0 Pochhammer 1 2 𝜇 𝜅 𝑠 Pochhammer 1 2 𝜇 𝜅 𝑠 𝑠 superscript 𝑥 𝑠 {\displaystyle{\displaystyle M_{\kappa,\mu}\left(x\right)\sim\frac{\Gamma\left% (1+2\mu\right)}{\Gamma\left(\frac{1}{2}+\mu-\kappa\right)}e^{\frac{1}{2}x}x^{-% \kappa}\*\sum_{s=0}^{\infty}\frac{{\left(\frac{1}{2}-\mu+\kappa\right)_{s}}{% \left(\frac{1}{2}+\mu+\kappa\right)_{s}}}{s!}x^{-s},}}
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    DLMF id
    DLMF:13.19.E1
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