DLMF:10.49.E20 (Q3724): Difference between revisions

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Property / Symbols used: DLMF:10.49.E17 / rank
 
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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.m1bdec

Latest revision as of 14:12, 2 January 2020

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DLMF:10.49.E20
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    Statements

    test
    ( 𝗂 n ( 1 ) ⁡ ( z ) ) 2 - ( 𝗂 n ( 2 ) ⁡ ( z ) ) 2 = ( - 1 ) n + 1 ⁢ ∑ k = 0 n ( - 1 ) k ⁢ s k ⁢ ( n + 1 2 ) z 2 ⁢ k + 2 . superscript spherical-Bessel-I-1 𝑛 𝑧 2 superscript spherical-Bessel-I-2 𝑛 𝑧 2 superscript 1 𝑛 1 superscript subscript 𝑘 0 𝑛 superscript 1 𝑘 subscript 𝑠 𝑘 𝑛 1 2 superscript 𝑧 2 𝑘 2 {\displaystyle{\displaystyle\left({\mathsf{i}^{(1)}_{n}}\left(z\right)\right)^% {2}-\left({\mathsf{i}^{(2)}_{n}}\left(z\right)\right)^{2}=(-1)^{n+1}\sum_{k=0}% ^{n}(-1)^{k}\frac{s_{k}(n+\frac{1}{2})}{z^{2k+2}}.}}
    0 references
    DLMF id
    DLMF:10.49.E20
    0 references
    Symbols used
    modified spherical Bessel function
    test
    𝗂 n ( 1 ) ⁡ ( z ) spherical-Bessel-I-1 𝑛 𝑧 {\displaystyle{\displaystyle{\mathsf{i}^{(1)}_{\NVar{n}}}\left(\NVar{z}\right)}}
    xml-id
    C10.S47.E7.m2acdec
    0 references
    modified spherical Bessel function
    test
    𝗂 n ( 2 ) ⁡ ( z ) spherical-Bessel-I-2 𝑛 𝑧 {\displaystyle{\displaystyle{\mathsf{i}^{(2)}_{\NVar{n}}}\left(\NVar{z}\right)}}
    xml-id
    C10.S47.E8.m2acdec
    0 references
    Q11429
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C10.S1.XMD2.m1mdec
    0 references
    Q11428
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C10.S1.XMD3.m1jdec
    0 references
    Q11426
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1qdec
    0 references
    DLMF:10.49.E17
    test
    s k ⁢ ( n ) subscript 𝑠 𝑘 𝑛 {\displaystyle{\displaystyle s_{k}(n)}}
    xml-id
    C10.S49.XMD1.m1bdec
    0 references
     
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