DLMF:18.10.E6 (Q5630)

From testwiki
Revision as of 15:06, 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:18.10.E6
No description defined

    Statements

    test
    L n ( α ) ⁡ ( x 2 ) = 2 ⁢ ( - 1 ) n π 1 2 ⁢ Γ ⁡ ( α + 1 2 ) ⁢ n ! ⁢ ∫ 0 ∞ ∫ 0 π ( x 2 - r 2 + 2 ⁢ i ⁢ x ⁢ r ⁢ cos ⁡ ϕ ) n ⁢ e - r 2 ⁢ r 2 ⁢ α + 1 ⁢ ( sin ⁡ ϕ ) 2 ⁢ α ⁢ d ϕ ⁢ d r , Laguerre-polynomial-L 𝛼 𝑛 superscript 𝑥 2 2 superscript 1 𝑛 superscript 𝜋 1 2 Euler-Gamma 𝛼 1 2 𝑛 superscript subscript 0 superscript subscript 0 𝜋 superscript superscript 𝑥 2 superscript 𝑟 2 2 𝑖 𝑥 𝑟 italic-ϕ 𝑛 superscript 𝑒 superscript 𝑟 2 superscript 𝑟 2 𝛼 1 superscript italic-ϕ 2 𝛼 italic-ϕ 𝑟 {\displaystyle{\displaystyle L^{(\alpha)}_{n}\left(x^{2}\right)=\frac{2(-1)^{n% }}{\pi^{\frac{1}{2}}\Gamma\left(\alpha+\tfrac{1}{2}\right)n!}\*\int_{0}^{% \infty}\int_{0}^{\pi}{(x^{2}-r^{2}+2ixr\cos\phi)^{n}}\*e^{-r^{2}}r^{2\alpha+1}% (\sin\phi)^{2\alpha}\mathrm{d}\phi\mathrm{d}r,}}
    0 references
    DLMF id
    DLMF:18.10.E6
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q5630&oldid=32150"