DLMF:9.13.E20 (Q2983): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11419 / rank
 
Normal rank
Property / Symbols used: Q11419 / qualifier
 
Defining formula:

U i subscript 𝑈 𝑖 {\displaystyle{\displaystyle U_{i}}}

U_{i}
Property / Symbols used: Q11419 / qualifier
 
xml-id: C9.S13.XMD12.m1cdec

Latest revision as of 15:02, 2 January 2020

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DLMF:9.13.E20
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    Statements

    Defining formula
    U 1 ⁢ ( x , α ) = 1 ( α + 2 ) 1 / ( α + 2 ) ⁢ Γ ⁡ ( α + 1 α + 2 ) ⁢ x 1 / 2 ⁢ J - 1 / ( α + 2 ) ⁡ ( 2 α + 2 ⁢ x ( α + 2 ) / 2 ) , subscript 𝑈 1 𝑥 𝛼 1 superscript 𝛼 2 1 𝛼 2 Euler-Gamma 𝛼 1 𝛼 2 superscript 𝑥 1 2 Bessel-J 1 𝛼 2 2 𝛼 2 superscript 𝑥 𝛼 2 2 {\displaystyle{\displaystyle U_{1}(x,\alpha)=\frac{1}{(\alpha+2)^{1/(\alpha+2)% }}\*\Gamma\left(\frac{\alpha+1}{\alpha+2}\right)x^{1/2}J_{-1/(\alpha+2)}\left(% \frac{2}{\alpha+2}x^{(\alpha+2)/2}\right),}}
    0 references
    DLMF id
    DLMF:9.13.E20
    0 references
    Symbols used
    Bessel function of the first kind
    Defining formula
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2abdec
    0 references
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
    0 references
    parameter (locally)
    Defining formula
    α 𝛼 {\displaystyle{\displaystyle\alpha}}
    xml-id
    C9.S13.XMD10.m1adec
    0 references
    parameter (locally)
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C9.S13.XMD11.m1adec
    0 references
    Q11419
    Defining formula
    U i subscript 𝑈 𝑖 {\displaystyle{\displaystyle U_{i}}}
    xml-id
    C9.S13.XMD12.m1cdec
    0 references
     
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