DLMF:10.60.E11 (Q3786): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: sine integral / rank
 
Normal rank
Property / Symbols used: sine integral / qualifier
 
test:

Si ( z ) sine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{Si}\left(\NVar{z}\right)}}

\sinint@{\NVar{z}}
Property / Symbols used: sine integral / qualifier
 
xml-id: C6.S2.E9.m2adec
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.m2afdec
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.m1jdec
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.m1gdec

Latest revision as of 14:19, 2 January 2020

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DLMF:10.60.E11
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    Statements

    n = 0 𝗃 n 2 ( z ) = Si ( 2 z ) 2 z . superscript subscript 𝑛 0 spherical-Bessel-J 𝑛 2 𝑧 sine-integral 2 𝑧 2 𝑧 {\displaystyle{\displaystyle\sum_{n=0}^{\infty}{\mathsf{j}_{n}^{2}}\left(z% \right)=\frac{\mathrm{Si}\left(2z\right)}{2z}.}}
    0 references
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    Si ( z ) sine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{Si}\left(\NVar{z}\right)}}
    C6.S2.E9.m2adec
    0 references
    𝗃 n ( z ) spherical-Bessel-J 𝑛 𝑧 {\displaystyle{\displaystyle\mathsf{j}_{\NVar{n}}\left(\NVar{z}\right)}}
    C10.S47.E3.m2afdec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C10.S1.XMD2.m1jdec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C10.S1.XMD6.m1gdec
    0 references