DLMF:10.35.E2 (Q3551): 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
Property / Symbols used
 
Property / Symbols used: Q11428 / rank
 
Normal rank
Property / Symbols used: Q11428 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11428 / qualifier
 
xml-id: C10.S1.XMD3.m1dec
Property / Symbols used
 
Property / Symbols used: Q11426 / rank
 
Normal rank
Property / Symbols used: Q11426 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11426 / qualifier
 
xml-id: C10.S1.XMD6.m1adec

Latest revision as of 12:48, 2 January 2020

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DLMF:10.35.E2
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    Statements

    e z cos θ = I 0 ( z ) + 2 k = 1 I k ( z ) cos ( k θ ) , superscript 𝑒 𝑧 𝜃 modified-Bessel-first-kind 0 𝑧 2 superscript subscript 𝑘 1 modified-Bessel-first-kind 𝑘 𝑧 𝑘 𝜃 {\displaystyle{\displaystyle e^{z\cos\theta}=I_{0}\left(z\right)+2\sum_{k=1}^{% \infty}I_{k}\left(z\right)\cos\left(k\theta\right),}}
    0 references
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    cos z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    C4.S14.E2.m2adec
    0 references
    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2aadec
    0 references
    I ν ( z ) modified-Bessel-first-kind 𝜈 𝑧 {\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}
    C10.S25.E2.m2aadec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C10.S1.XMD3.m1dec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C10.S1.XMD6.m1adec
    0 references