DLMF:6.10.E4 (Q2281): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: sine integral / rank
 
Normal rank
Property / Symbols used: sine integral / qualifier
 
Defining formula:

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
 
Defining formula:

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: Q11305 / rank
 
Normal rank
Property / Symbols used: Q11305 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11305 / qualifier
 
xml-id: C6.S1.XMD2.m1adec
Property / Symbols used
 
Property / Symbols used: Q11308 / rank
 
Normal rank
Property / Symbols used: Q11308 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11308 / qualifier
 
xml-id: C6.S1.XMD3.m1dec

Latest revision as of 01:30, 2 January 2020

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DLMF:6.10.E4
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    Statements

    Si ( z ) = z n = 0 ( 𝗃 n ( 1 2 z ) ) 2 , sine-integral 𝑧 𝑧 superscript subscript 𝑛 0 superscript spherical-Bessel-J 𝑛 1 2 𝑧 2 {\displaystyle{\displaystyle\mathrm{Si}\left(z\right)=z\sum_{n=0}^{\infty}% \left(\mathsf{j}_{n}\left(\tfrac{1}{2}z\right)\right)^{2},}}
    0 references
    DLMF:6.10.E4
    0 references
    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.m2adec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C6.S1.XMD2.m1adec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C6.S1.XMD3.m1dec
    0 references