DLMF:10.53.E2 (Q3756): Difference between revisions

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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.m2adec

Revision as of 14:14, 2 January 2020

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DLMF:10.53.E2
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    Statements

    test
    𝗒 n ⁡ ( z ) = - 1 z n + 1 ⁢ ∑ k = 0 n ( 2 ⁢ n - 2 ⁢ k - 1 ) !! ⁢ ( 1 2 ⁢ z 2 ) k k ! + ( - 1 ) n + 1 z n + 1 ⁢ ∑ k = n + 1 ∞ ( - 1 2 ⁢ z 2 ) k k ! ⁢ ( 2 ⁢ k - 2 ⁢ n - 1 ) !! . spherical-Bessel-Y 𝑛 𝑧 1 superscript 𝑧 𝑛 1 superscript subscript 𝑘 0 𝑛 double-factorial 2 𝑛 2 𝑘 1 superscript 1 2 superscript 𝑧 2 𝑘 𝑘 superscript 1 𝑛 1 superscript 𝑧 𝑛 1 superscript subscript 𝑘 𝑛 1 superscript 1 2 superscript 𝑧 2 𝑘 𝑘 double-factorial 2 𝑘 2 𝑛 1 {\displaystyle{\displaystyle\mathsf{y}_{n}\left(z\right)=-\frac{1}{z^{n+1}}% \sum_{k=0}^{n}\frac{(2n-2k-1)!!(\frac{1}{2}z^{2})^{k}}{k!}+\frac{(-1)^{n+1}}{z% ^{n+1}}\sum_{k=n+1}^{\infty}\frac{(-\frac{1}{2}z^{2})^{k}}{k!(2k-2n-1)!!}.}}
    0 references
    DLMF id
    DLMF:10.53.E2
    0 references
    constraint
    0 < | z | < ∞ . 0 𝑧 {\displaystyle{\displaystyle 0<|z|<\infty.}}
    0 references
    Symbols used
    Q11277
    test
    !! double-factorial {\displaystyle{\displaystyle!!}}
    xml-id
    introduction.Sx4.p1.t1.r16.m7aadec
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    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
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    spherical Bessel function of the second kind
    test
    𝗒 n ⁡ ( z ) spherical-Bessel-Y 𝑛 𝑧 {\displaystyle{\displaystyle\mathsf{y}_{\NVar{n}}\left(\NVar{z}\right)}}
    xml-id
    C10.S47.E4.m2adec
    0 references
     
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