DLMF:10.47.E13 (Q3683): 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.m1ldec

Latest 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
    modified spherical Bessel function
    test
    𝗄 n ⁡ ( z ) spherical-Bessel-K 𝑛 𝑧 {\displaystyle{\displaystyle\mathsf{k}_{\NVar{n}}\left(\NVar{z}\right)}}
    xml-id
    C10.S47.E9.m2abdec
    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.m2abdec
    0 references
    spherical Bessel function of the third kind
    test
    𝗁 n ( 2 ) ⁡ ( z ) spherical-Hankel-H-2-Bessel-third-kind 𝑛 𝑧 {\displaystyle{\displaystyle{\mathsf{h}^{(2)}_{\NVar{n}}}\left(\NVar{z}\right)}}
    xml-id
    C10.S47.E6.m2abdec
    0 references
    Q11429
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C10.S1.XMD2.m1ldec
    0 references
    Q11426
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1ldec
    0 references
     
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