DLMF:10.9.E23 (Q3093): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
test:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2akdec

Revision as of 15:16, 2 January 2020

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DLMF:10.9.E23
No description defined

    Statements

    test
    J ν ⁡ ( z ) = 1 2 ⁢ π ⁢ i ⁢ ∫ - ∞ - i ⁢ c - ∞ + i ⁢ c Γ ⁡ ( t ) Γ ⁡ ( ν - t + 1 ) ⁢ ( 1 2 ⁢ z ) ν - 2 ⁢ t ⁢ d t , Bessel-J 𝜈 𝑧 1 2 𝜋 𝑖 superscript subscript 𝑖 𝑐 𝑖 𝑐 Euler-Gamma 𝑡 Euler-Gamma 𝜈 𝑡 1 superscript 1 2 𝑧 𝜈 2 𝑡 𝑡 {\displaystyle{\displaystyle J_{\nu}\left(z\right)=\frac{1}{2\pi i}\int_{-% \infty-ic}^{-\infty+ic}\frac{\Gamma\left(t\right)}{\Gamma\left(\nu-t+1\right)}% (\tfrac{1}{2}z)^{\nu-2t}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:10.9.E23
    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.m2aldec
    0 references
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2afdec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2avdec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1avdec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2akdec
    0 references
     
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