DLMF:10.8.E3 (Q3065): 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.m2adec

Revision as of 15:10, 2 January 2020

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DLMF:10.8.E3
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    Statements

    test
    J ν ⁡ ( z ) ⁢ J μ ⁡ ( z ) = ( 1 2 ⁢ z ) ν + μ ⁢ ∑ k = 0 ∞ ( ν + μ + k + 1 ) k ⁢ ( - 1 4 ⁢ z 2 ) k k ! ⁢ Γ ⁡ ( ν + k + 1 ) ⁢ Γ ⁡ ( μ + k + 1 ) . Bessel-J 𝜈 𝑧 Bessel-J 𝜇 𝑧 superscript 1 2 𝑧 𝜈 𝜇 superscript subscript 𝑘 0 subscript 𝜈 𝜇 𝑘 1 𝑘 superscript 1 4 superscript 𝑧 2 𝑘 𝑘 Euler-Gamma 𝜈 𝑘 1 Euler-Gamma 𝜇 𝑘 1 {\displaystyle{\displaystyle J_{\nu}\left(z\right)J_{\mu}\left(z\right)=(% \tfrac{1}{2}z)^{\nu+\mu}\sum_{k=0}^{\infty}\frac{(\nu+\mu+k+1)_{k}(-\tfrac{1}{% 4}z^{2})^{k}}{k!\Gamma\left(\nu+k+1\right)\Gamma\left(\mu+k+1\right)}.}}
    0 references
    DLMF id
    DLMF:10.8.E3
    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.m2abdec
    0 references
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    0 references
     
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