DLMF:10.39.E7 (Q3575)

From testwiki
Revision as of 13:51, 2 January 2020 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:10.39.E7
No description defined

    Statements

    test
    I ν ⁡ ( z ) = ( 2 ⁢ z ) - 1 2 ⁢ M 0 , ν ⁡ ( 2 ⁢ z ) 2 2 ⁢ ν ⁢ Γ ⁡ ( ν + 1 ) , modified-Bessel-first-kind 𝜈 𝑧 superscript 2 𝑧 1 2 Whittaker-confluent-hypergeometric-M 0 𝜈 2 𝑧 superscript 2 2 𝜈 Euler-Gamma 𝜈 1 {\displaystyle{\displaystyle I_{\nu}\left(z\right)=\frac{(2z)^{-\frac{1}{2}}M_% {0,\nu}\left(2z\right)}{2^{2\nu}\Gamma\left(\nu+1\right)},}}
    0 references
    DLMF id
    DLMF:10.39.E7
    0 references
    constraint
    2 ⁢ ν ≠ - 1 , - 2 , - 3 , … 2 𝜈 1 2 3 … {\displaystyle{\displaystyle 2\nu\neq-1,-2,-3,\dots}}
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
    0 references
    Whittaker confluent hypergeometric function
    test
    M κ , μ ⁡ ( z ) Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}
    xml-id
    C13.S14.E2.m2adec
    0 references
    modified Bessel function of the first kind
    test
    I ν ⁡ ( z ) modified-Bessel-first-kind 𝜈 𝑧 {\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S25.E2.m2abdec
    0 references
    Q11426
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1fdec
    0 references
    Q11427
    test
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1bdec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q3575&oldid=19114"