DLMF:10.35.E1 (Q3550): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2adec
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.m2adec
Property / Symbols used
 
Property / Symbols used: Q11438 / rank
 
Normal rank
Property / Symbols used: Q11438 / qualifier
 
test:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q11438 / qualifier
 
xml-id: C10.S1.XMD1.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.m1dec

Latest revision as of 13:47, 2 January 2020

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DLMF:10.35.E1
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    Statements

    e 1 2 z ( t + t - 1 ) = m = - t m I m ( z ) . superscript 𝑒 1 2 𝑧 𝑡 superscript 𝑡 1 superscript subscript 𝑚 superscript 𝑡 𝑚 modified-Bessel-first-kind 𝑚 𝑧 {\displaystyle{\displaystyle e^{\frac{1}{2}z(t+t^{-1})}=\sum_{m=-\infty}^{% \infty}t^{m}I_{m}\left(z\right).}}
    0 references
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    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2adec
    0 references
    I ν ( z ) modified-Bessel-first-kind 𝜈 𝑧 {\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}
    C10.S25.E2.m2adec
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    m 𝑚 {\displaystyle{\displaystyle m}}
    C10.S1.XMD1.m1dec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C10.S1.XMD6.m1dec
    0 references