DLMF:13.16.E4 (Q4555): Difference between revisions

From testwiki
Jump to navigation Jump to search
← Older editNewer edit →
imported>Admin
imported>Admin
Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
test:

Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

\EulerGamma@{\NVar{z}}
Property / Symbols used: gamma function / qualifier
 
xml-id: C5.S2.E1.m2acdec

Revision as of 15:10, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:13.16.E4
No description defined

    Statements

    test
    1 Γ ⁡ ( 1 + 2 ⁢ μ ) ⁢ M κ , μ ⁡ ( z ) = z ⁢ e - 1 2 ⁢ z Γ ⁡ ( 1 2 + μ - κ ) ⁢ ∫ 0 ∞ e - t ⁢ t - κ - 1 2 ⁢ I 2 ⁢ μ ⁡ ( 2 ⁢ z ⁢ t ) ⁢ d t , 1 Euler-Gamma 1 2 𝜇 Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 𝑧 superscript 𝑒 1 2 𝑧 Euler-Gamma 1 2 𝜇 𝜅 superscript subscript 0 superscript 𝑒 𝑡 superscript 𝑡 𝜅 1 2 modified-Bessel-first-kind 2 𝜇 2 𝑧 𝑡 𝑡 {\displaystyle{\displaystyle\frac{1}{\Gamma\left(1+2\mu\right)}M_{\kappa,\mu}% \left(z\right)=\frac{\sqrt{z}e^{-\frac{1}{2}z}}{\Gamma\left(\frac{1}{2}+\mu-% \kappa\right)}\*\int_{0}^{\infty}e^{-t}t^{-\kappa-\frac{1}{2}}I_{2\mu}\left(2% \sqrt{zt}\right)\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:13.16.E4
    0 references
    constraint
    ℜ ⁡ ( κ - μ ) - 1 2 < 0 𝜅 𝜇 1 2 0 {\displaystyle{\displaystyle\Re(\kappa-\mu)-\tfrac{1}{2}<0}}
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2acdec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q4555&oldid=24959"