DLMF:10.34.E6 (Q3547): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: modified Bessel function of the second kind / rank
 
Normal rank
Property / Symbols used: modified Bessel function of the second kind / qualifier
 
test:

K ν ⁡ ( z ) modified-Bessel-second-kind 𝜈 𝑧 {\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}

\modBesselK{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: modified Bessel function of the second kind / qualifier
 
xml-id: C10.S25.E3.m2addec
Property / Symbols used
 
Property / Symbols used: Q11438 / rank
 
Normal rank
Property / Symbols used: Q11438 / qualifier
 
test:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q11438 / qualifier
 
xml-id: C10.S1.XMD1.m1edec
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.m1adec
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.m1edec

Latest revision as of 12:47, 2 January 2020

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Language Label Description Also known as
English
DLMF:10.34.E6
No description defined

    Statements

    test
    K n ⁡ ( z ⁢ e m ⁢ π ⁢ i ) = ± ( - 1 ) n ⁢ ( m - 1 ) ⁢ m ⁢ K n ⁡ ( z ⁢ e ± π ⁢ i ) ∓ ( - 1 ) n ⁢ m ⁢ ( m ∓ 1 ) ⁢ K n ⁡ ( z ) . modified-Bessel-second-kind 𝑛 𝑧 superscript 𝑒 𝑚 𝜋 𝑖 minus-or-plus plus-or-minus superscript 1 𝑛 𝑚 1 𝑚 modified-Bessel-second-kind 𝑛 𝑧 superscript 𝑒 plus-or-minus 𝜋 𝑖 superscript 1 𝑛 𝑚 minus-or-plus 𝑚 1 modified-Bessel-second-kind 𝑛 𝑧 {\displaystyle{\displaystyle K_{n}\left(ze^{m\pi i}\right)=\pm(-1)^{n(m-1)}mK_% {n}\left(ze^{\pm\pi i}\right)\mp(-1)^{nm}(m\mp 1)K_{n}\left(z\right).}}
    0 references
    DLMF id
    DLMF:10.34.E6
    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.m2aedec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aedec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aedec
    0 references
    modified Bessel function of the second kind
    test
    K ν ⁡ ( z ) modified-Bessel-second-kind 𝜈 𝑧 {\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S25.E3.m2addec
    0 references
    Q11438
    test
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C10.S1.XMD1.m1edec
    0 references
    Q11429
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C10.S1.XMD2.m1adec
    0 references
    Q11426
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1edec
    0 references
     
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