DLMF:10.44.E3 (Q3651): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: modified Bessel function of the first kind / rank
 
Normal rank
Property / Symbols used: modified Bessel function of the first kind / qualifier
 
test:

I ν ⁡ ( z ) modified-Bessel-first-kind 𝜈 𝑧 {\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}

\modBesselI{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: modified Bessel function of the first kind / qualifier
 
xml-id: C10.S25.E2.m2aadec

Revision as of 13:05, 2 January 2020

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DLMF:10.44.E3
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    Statements

    test
    𝒵 ν ⁡ ( u ± v ) = ∑ k = - ∞ ∞ ( ± 1 ) k ⁢ 𝒵 ν + k ⁡ ( u ) ⁢ I k ⁡ ( v ) , modified-cylinder-function 𝜈 plus-or-minus 𝑢 𝑣 superscript subscript 𝑘 superscript plus-or-minus 1 𝑘 modified-cylinder-function 𝜈 𝑘 𝑢 modified-Bessel-first-kind 𝑘 𝑣 {\displaystyle{\displaystyle\mathscr{Z}_{\nu}\left(u\pm v\right)=\sum_{k=-% \infty}^{\infty}(\pm 1)^{k}\mathscr{Z}_{\nu+k}\left(u\right)I_{k}\left(v\right% ),}}
    0 references
    DLMF id
    DLMF:10.44.E3
    0 references
    constraint
    | v | < | u | 𝑣 𝑢 {\displaystyle{\displaystyle|v|<|u|}}
    0 references
    Symbols used
    modified Bessel function of the first kind
    test
    I ν ⁡ ( z ) modified-Bessel-first-kind 𝜈 𝑧 {\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S25.E2.m2aadec
    0 references
     
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