DLMF:10.35.E3 (Q3552): 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.m2abdec

Revision as of 12:48, 2 January 2020

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DLMF:10.35.E3
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    Statements

    test
    e z ⁢ sin ⁡ θ = I 0 ⁡ ( z ) + 2 ⁢ ∑ k = 0 ∞ ( - 1 ) k ⁢ I 2 ⁢ k + 1 ⁡ ( z ) ⁢ sin ⁡ ( ( 2 ⁢ k + 1 ) ⁢ θ ) + 2 ⁢ ∑ k = 1 ∞ ( - 1 ) k ⁢ I 2 ⁢ k ⁡ ( z ) ⁢ cos ⁡ ( 2 ⁢ k ⁢ θ ) . superscript 𝑒 𝑧 𝜃 modified-Bessel-first-kind 0 𝑧 2 superscript subscript 𝑘 0 superscript 1 𝑘 modified-Bessel-first-kind 2 𝑘 1 𝑧 2 𝑘 1 𝜃 2 superscript subscript 𝑘 1 superscript 1 𝑘 modified-Bessel-first-kind 2 𝑘 𝑧 2 𝑘 𝜃 {\displaystyle{\displaystyle e^{z\sin\theta}=I_{0}\left(z\right)+2\sum_{k=0}^{% \infty}(-1)^{k}I_{2k+1}\left(z\right)\sin\left((2k+1)\theta\right)+2\sum_{k=1}% ^{\infty}(-1)^{k}I_{2k}\left(z\right)\cos\left(2k\theta\right).}}
    0 references
    DLMF id
    DLMF:10.35.E3
    0 references
    Symbols used
    cosine function
    test
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
    0 references
     
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