DLMF:10.16.E9 (Q3168): Difference between revisions

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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.m2abdec

Revision as of 15:27, 2 January 2020

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DLMF:10.16.E9
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    Statements

    test
    J ν ⁡ ( z ) = ( 1 2 ⁢ z ) ν Γ ⁡ ( ν + 1 ) ⁢ F 1 0 ⁡ ( - ; ν + 1 ; - 1 4 ⁢ z 2 ) . Bessel-J 𝜈 𝑧 superscript 1 2 𝑧 𝜈 Euler-Gamma 𝜈 1 Gauss-hypergeometric-pFq 0 1 𝜈 1 1 4 superscript 𝑧 2 {\displaystyle{\displaystyle J_{\nu}\left(z\right)=\frac{(\tfrac{1}{2}z)^{\nu}% }{\Gamma\left(\nu+1\right)}{{}_{0}F_{1}}\left(-;\nu+1;-\tfrac{1}{4}z^{2}\right% ).}}
    0 references
    DLMF id
    DLMF:10.16.E9
    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.m2aedec
    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
     
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