DLMF:13.16.E8 (Q4559)

From testwiki
Revision as of 14:30, 29 December 2019 by imported>Admin (Admin moved page Main Page to Verifying DLMF with Maple and Mathematica)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:13.16.E8
No description defined

    Statements

    test
    W κ , μ ⁡ ( z ) = 2 ⁢ z ⁢ e - 1 2 ⁢ z Γ ⁡ ( 1 2 + μ - κ ) ⁢ Γ ⁡ ( 1 2 - μ - κ ) ⁢ ∫ 0 ∞ e - t ⁢ t - κ - 1 2 ⁢ K 2 ⁢ μ ⁡ ( 2 ⁢ z ⁢ t ) ⁢ d t , Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑧 2 𝑧 superscript 𝑒 1 2 𝑧 Euler-Gamma 1 2 𝜇 𝜅 Euler-Gamma 1 2 𝜇 𝜅 superscript subscript 0 superscript 𝑒 𝑡 superscript 𝑡 𝜅 1 2 modified-Bessel-second-kind 2 𝜇 2 𝑧 𝑡 𝑡 {\displaystyle{\displaystyle W_{\kappa,\mu}\left(z\right)=\frac{2\sqrt{z}e^{-% \frac{1}{2}z}}{\Gamma\left(\frac{1}{2}+\mu-\kappa\right)\Gamma\left(\frac{1}{2% }-\mu-\kappa\right)}\*\int_{0}^{\infty}e^{-t}t^{-\kappa-\frac{1}{2}}K_{2\mu}% \left(2\sqrt{zt}\right)\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:13.16.E8
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q4559&oldid=25018"