DLMF:10.23.E15 (Q3469): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11427 / rank
 
Normal rank
Property / Symbols used: Q11427 / qualifier
 
test:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11427 / qualifier
 
xml-id: C10.S1.XMD7.m1fdec

Latest revision as of 13:31, 2 January 2020

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DLMF:10.23.E15
No description defined

    Statements

    test
    ( 1 2 ⁢ z ) ν = ∑ k = 0 ∞ ( ν + 2 ⁢ k ) ⁢ Γ ⁡ ( ν + k ) k ! ⁢ J ν + 2 ⁢ k ⁡ ( z ) , superscript 1 2 𝑧 𝜈 superscript subscript 𝑘 0 𝜈 2 𝑘 Euler-Gamma 𝜈 𝑘 𝑘 Bessel-J 𝜈 2 𝑘 𝑧 {\displaystyle{\displaystyle(\tfrac{1}{2}z)^{\nu}=\sum_{k=0}^{\infty}\frac{(% \nu+2k)\Gamma\left(\nu+k\right)}{k!}J_{\nu+2k}\left(z\right),}}
    0 references
    DLMF id
    DLMF:10.23.E15
    0 references
    constraint
    ν ≠ 0 , - 1 , - 2 , … 𝜈 0 1 2 … {\displaystyle{\displaystyle\nu\neq 0,-1,-2,\dots}}
    0 references
    Symbols used
    Bessel function of the first kind
    test
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2ajdec
    0 references
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2abdec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5abdec
    0 references
    Q11428
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C10.S1.XMD3.m1mdec
    0 references
    Q11426
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1hdec
    0 references
    Q11427
    test
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1fdec
    0 references
     
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