DLMF:10.49.E18 (Q3720): 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.m2acdec
Property / Symbols used
 
Property / Symbols used: spherical Bessel function of the second kind / rank
 
Normal rank
Property / Symbols used: spherical Bessel function of the second kind / qualifier
 
test:

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

\sphBesselY{\NVar{n}}@{\NVar{z}}
Property / Symbols used: spherical Bessel function of the second kind / qualifier
 
xml-id: C10.S47.E4.m2acdec
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.m1ldec
Property / Symbols used
 
Property / Symbols used: Q11428 / rank
 
Normal rank
Property / Symbols used: Q11428 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11428 / qualifier
 
xml-id: C10.S1.XMD3.m1idec
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.m1odec
Property / Symbols used
 
Property / Symbols used: DLMF:10.49.E17 / rank
 
Normal rank
Property / Symbols used: DLMF:10.49.E17 / qualifier
 
test:

s k ( n ) subscript 𝑠 𝑘 𝑛 {\displaystyle{\displaystyle s_{k}(n)}}

s_{k}(n)
Property / Symbols used: DLMF:10.49.E17 / qualifier
 
xml-id: C10.S49.XMD1.m1adec

Latest revision as of 13:12, 2 January 2020

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DLMF:10.49.E18
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    Statements

    𝗃 n 2 ( z ) + 𝗒 n 2 ( z ) = k = 0 n s k ( n + 1 2 ) z 2 k + 2 . spherical-Bessel-J 𝑛 2 𝑧 spherical-Bessel-Y 𝑛 2 𝑧 superscript subscript 𝑘 0 𝑛 subscript 𝑠 𝑘 𝑛 1 2 superscript 𝑧 2 𝑘 2 {\displaystyle{\displaystyle{\mathsf{j}_{n}^{2}}\left(z\right)+{\mathsf{y}_{n}% ^{2}}\left(z\right)=\sum_{k=0}^{n}\frac{s_{k}(n+\frac{1}{2})}{z^{2k+2}}.}}
    0 references
    0 references
    𝗃 n ( z ) spherical-Bessel-J 𝑛 𝑧 {\displaystyle{\displaystyle\mathsf{j}_{\NVar{n}}\left(\NVar{z}\right)}}
    C10.S47.E3.m2acdec
    0 references
    𝗒 n ( z ) spherical-Bessel-Y 𝑛 𝑧 {\displaystyle{\displaystyle\mathsf{y}_{\NVar{n}}\left(\NVar{z}\right)}}
    C10.S47.E4.m2acdec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C10.S1.XMD2.m1ldec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C10.S1.XMD3.m1idec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C10.S1.XMD6.m1odec
    0 references
    s k ( n ) subscript 𝑠 𝑘 𝑛 {\displaystyle{\displaystyle s_{k}(n)}}
    C10.S49.XMD1.m1adec
    0 references