DLMF:10.53.E4 (Q3758): Difference between revisions

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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.m1cdec

Revision as of 14:14, 2 January 2020

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DLMF:10.53.E4
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    Statements

    test
    𝗂 n ( 2 ) ⁡ ( z ) = ( - 1 ) n z n + 1 ⁢ ∑ k = 0 n ( 2 ⁢ n - 2 ⁢ k - 1 ) !! ⁢ ( - 1 2 ⁢ z 2 ) k k ! + 1 z n + 1 ⁢ ∑ k = n + 1 ∞ ( 1 2 ⁢ z 2 ) k k ! ⁢ ( 2 ⁢ k - 2 ⁢ n - 1 ) !! . spherical-Bessel-I-2 𝑛 𝑧 superscript 1 𝑛 superscript 𝑧 𝑛 1 superscript subscript 𝑘 0 𝑛 double-factorial 2 𝑛 2 𝑘 1 superscript 1 2 superscript 𝑧 2 𝑘 𝑘 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{i}^{(2)}_{n}}\left(z\right)=\frac{(-1)^{n% }}{z^{n+1}}\sum_{k=0}^{n}\frac{(2n-2k-1)!!(-\frac{1}{2}z^{2})^{k}}{k!}+\frac{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.E4
    0 references
    constraint
    0 < | z | < ∞ . 0 𝑧 {\displaystyle{\displaystyle 0<|z|<\infty.}}
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    Symbols used
    Q11277
    test
    !! double-factorial {\displaystyle{\displaystyle!!}}
    xml-id
    introduction.Sx4.p1.t1.r16.m7acdec
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    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5acdec
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    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.m2adec
    0 references
    Q11429
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C10.S1.XMD2.m1cdec
    0 references
     
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