DLMF:10.49.E6 (Q3700): Difference between revisions

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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.m1ddec
Property / Symbols used
 
Property / Symbols used: expansion (locally) / rank
 
Normal rank
Property / Symbols used: expansion (locally) / qualifier
 
test:

a k ⁢ ( ν ) subscript 𝑎 𝑘 𝜈 {\displaystyle{\displaystyle a_{k}(\nu)}}

a_{k}(\nu)
Property / Symbols used: expansion (locally) / qualifier
 
xml-id: C10.S17.XMD1.m1cdec

Latest revision as of 14:10, 2 January 2020

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DLMF:10.49.E6
No description defined

    Statements

    test
    𝗁 n ( 1 ) ⁡ ( z ) = e i ⁢ z ⁢ ∑ k = 0 n i k - n - 1 ⁢ a k ⁢ ( n + 1 2 ) z k + 1 , spherical-Hankel-H-1-Bessel-third-kind 𝑛 𝑧 superscript 𝑒 𝑖 𝑧 superscript subscript 𝑘 0 𝑛 superscript 𝑖 𝑘 𝑛 1 subscript 𝑎 𝑘 𝑛 1 2 superscript 𝑧 𝑘 1 {\displaystyle{\displaystyle{\mathsf{h}^{(1)}_{n}}\left(z\right)=e^{iz}\sum_{k% =0}^{n}i^{k-n-1}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}},}}
    0 references
    DLMF id
    DLMF:10.49.E6
    0 references
    Symbols used
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    spherical Bessel function of the third kind
    test
    𝗁 n ( 1 ) ⁡ ( z ) spherical-Hankel-H-1-Bessel-third-kind 𝑛 𝑧 {\displaystyle{\displaystyle{\mathsf{h}^{(1)}_{\NVar{n}}}\left(\NVar{z}\right)}}
    xml-id
    C10.S47.E5.m2adec
    0 references
    Q11429
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C10.S1.XMD2.m1cdec
    0 references
    Q11428
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C10.S1.XMD3.m1cdec
    0 references
    Q11426
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1ddec
    0 references
    expansion (locally)
    test
    a k ⁢ ( ν ) subscript 𝑎 𝑘 𝜈 {\displaystyle{\displaystyle a_{k}(\nu)}}
    xml-id
    C10.S17.XMD1.m1cdec
    0 references
     
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