DLMF:10.44.E4 (Q3652): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
test:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5abdec

Revision as of 14:05, 2 January 2020

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English
DLMF:10.44.E4
No description defined

    Statements

    test
    ( 1 2 ⁢ z ) ν = ∑ k = 0 ∞ ( - 1 ) k ⁢ ( ν + 2 ⁢ k ) ⁢ Γ ⁡ ( ν + k ) k ! ⁢ I ν + 2 ⁢ k ⁡ ( z ) , superscript 1 2 𝑧 𝜈 superscript subscript 𝑘 0 superscript 1 𝑘 𝜈 2 𝑘 Euler-Gamma 𝜈 𝑘 𝑘 modified-Bessel-first-kind 𝜈 2 𝑘 𝑧 {\displaystyle{\displaystyle\left(\tfrac{1}{2}z\right)^{\nu}=\sum_{k=0}^{% \infty}(-1)^{k}\frac{(\nu+2k)\Gamma\left(\nu+k\right)}{k!}I_{\nu+2k}\left(z% \right),}}
    0 references
    DLMF id
    DLMF:10.44.E4
    0 references
    constraint
    ν ≠ 0 , - 1 , - 2 , … 𝜈 0 1 2 … {\displaystyle{\displaystyle\nu\neq 0,-1,-2,\ldots}}
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5abdec
    0 references
     
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