DLMF:10.32.E16 (Q3536): Difference between revisions

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Property / constraint
 

ℜ ⁡ ( μ ∓ ν ) > - 1 2 minus-or-plus 𝜇 𝜈 1 2 {\displaystyle{\displaystyle\Re(\mu\mp\nu)>-\tfrac{1}{2}}}

\Re(\mu\mp\nu)>-\tfrac{1}{2}
Property / constraint: ℜ ⁡ ( μ ∓ ν ) > - 1 2 minus-or-plus 𝜇 𝜈 1 2 {\displaystyle{\displaystyle\Re(\mu\mp\nu)>-\tfrac{1}{2}}} / rank
 
Normal rank

Revision as of 16:39, 30 December 2019

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DLMF:10.32.E16
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    Statements

    test
    I μ ⁡ ( x ) ⁢ K ν ⁡ ( x ) = ∫ 0 ∞ J μ ± ν ⁡ ( 2 ⁢ x ⁢ sinh ⁡ t ) ⁢ e ( - μ ± ν ) ⁢ t ⁢ d t , modified-Bessel-first-kind 𝜇 𝑥 modified-Bessel-second-kind 𝜈 𝑥 superscript subscript 0 Bessel-J plus-or-minus 𝜇 𝜈 2 𝑥 𝑡 superscript 𝑒 plus-or-minus 𝜇 𝜈 𝑡 𝑡 {\displaystyle{\displaystyle I_{\mu}\left(x\right)K_{\nu}\left(x\right)=\int_{% 0}^{\infty}J_{\mu\pm\nu}\left(2x\sinh t\right)e^{(-\mu\pm\nu)t}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:10.32.E16
    0 references
    constraint
    ℜ ⁡ ( μ ∓ ν ) > - 1 2 minus-or-plus 𝜇 𝜈 1 2 {\displaystyle{\displaystyle\Re(\mu\mp\nu)>-\tfrac{1}{2}}}
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    ℜ ⁡ ( μ ± ν ) > - 1 plus-or-minus 𝜇 𝜈 1 {\displaystyle{\displaystyle\Re(\mu\pm\nu)>-1}}
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    ℜ ⁡ ( μ ∓ ν ) > - 1 2 minus-or-plus 𝜇 𝜈 1 2 {\displaystyle{\displaystyle\Re(\mu\mp\nu)>-\tfrac{1}{2}}}
    0 references
     
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