DLMF:10.47.E13 (Q3683): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
test:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2addec

Revision as of 14:09, 2 January 2020

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DLMF:10.47.E13
No description defined

    Statements

    test
    𝗄 n ⁡ ( z ) = - 1 2 ⁢ π ⁢ i n ⁢ 𝗁 n ( 1 ) ⁡ ( i ⁢ z ) = - 1 2 ⁢ π ⁢ i - n ⁢ 𝗁 n ( 2 ) ⁡ ( - i ⁢ z ) . spherical-Bessel-K 𝑛 𝑧 1 2 𝜋 superscript 𝑖 𝑛 spherical-Hankel-H-1-Bessel-third-kind 𝑛 𝑖 𝑧 1 2 𝜋 superscript 𝑖 𝑛 spherical-Hankel-H-2-Bessel-third-kind 𝑛 𝑖 𝑧 {\displaystyle{\displaystyle\mathsf{k}_{n}\left(z\right)=-\tfrac{1}{2}\pi i^{n% }{\mathsf{h}^{(1)}_{n}}\left(iz\right)=-\tfrac{1}{2}\pi i^{-n}{\mathsf{h}^{(2)% }_{n}}\left(-iz\right).}}
    0 references
    DLMF id
    DLMF:10.47.E13
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ahdec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2addec
    0 references
     
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