DLMF:10.56.E1 (Q3765): Difference between revisions

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

𝗃 n ( z ) spherical-Bessel-J 𝑛 𝑧 {\displaystyle{\displaystyle\mathsf{j}_{\NVar{n}}\left(\NVar{z}\right)}}

\sphBesselJ{\NVar{n}}@{\NVar{z}}
Property / Symbols used: spherical Bessel function of the first kind / qualifier
 
xml-id: C10.S47.E3.m2adec
Property / Symbols used
 
Property / Symbols used: Q11429 / rank
 
Normal rank
Property / Symbols used: Q11429 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11429 / qualifier
 
xml-id: C10.S1.XMD2.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 14:16, 2 January 2020

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DLMF:10.56.E1
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    Statements

    cos z 2 - 2 z t z = cos z z + n = 1 t n n ! 𝗃 n - 1 ( z ) , superscript 𝑧 2 2 𝑧 𝑡 𝑧 𝑧 𝑧 superscript subscript 𝑛 1 superscript 𝑡 𝑛 𝑛 spherical-Bessel-J 𝑛 1 𝑧 {\displaystyle{\displaystyle\frac{\cos\sqrt{z^{2}-2zt}}{z}=\frac{\cos z}{z}+% \sum_{n=1}^{\infty}\frac{t^{n}}{n!}\mathsf{j}_{n-1}\left(z\right),}}
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    cos z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    C4.S14.E2.m2adec
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    ! {\displaystyle{\displaystyle!}}
    introduction.Sx4.p1.t1.r15.m5adec
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    𝗃 n ( z ) spherical-Bessel-J 𝑛 𝑧 {\displaystyle{\displaystyle\mathsf{j}_{\NVar{n}}\left(\NVar{z}\right)}}
    C10.S47.E3.m2adec
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    n 𝑛 {\displaystyle{\displaystyle n}}
    C10.S1.XMD2.m1dec
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    z 𝑧 {\displaystyle{\displaystyle z}}
    C10.S1.XMD6.m1dec
    0 references