DLMF:10.47.E5 (Q3673): 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.m2adec
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.m1ddec
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.m1ddec

Latest revision as of 13:08, 2 January 2020

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DLMF:10.47.E5
No description defined

    Statements

    test
    𝗁 n ( 1 ) ⁡ ( z ) = 1 2 ⁢ π / z ⁢ H n + 1 2 ( 1 ) ⁡ ( z ) = ( - 1 ) n + 1 ⁢ i ⁢ 1 2 ⁢ π / z ⁢ H - n - 1 2 ( 1 ) ⁡ ( z ) , spherical-Hankel-H-1-Bessel-third-kind 𝑛 𝑧 1 2 𝜋 𝑧 Hankel-H-1-Bessel-third-kind 𝑛 1 2 𝑧 superscript 1 𝑛 1 imaginary-unit 1 2 𝜋 𝑧 Hankel-H-1-Bessel-third-kind 𝑛 1 2 𝑧 {\displaystyle{\displaystyle{\mathsf{h}^{(1)}_{n}}\left(z\right)=\sqrt{\tfrac{% 1}{2}\pi/z}{H^{(1)}_{n+\frac{1}{2}}}\left(z\right)=(-1)^{n+1}\mathrm{i}\sqrt{% \tfrac{1}{2}\pi/z}{H^{(1)}_{-n-\frac{1}{2}}}\left(z\right),}}
    0 references
    DLMF id
    DLMF:10.47.E5
    0 references
    Symbols used
    Bessel function of the third kind (or Hankel function)
    test
    H ν ( 1 ) ⁡ ( z ) Hankel-H-1-Bessel-third-kind 𝜈 𝑧 {\displaystyle{\displaystyle{H^{(1)}_{\NVar{\nu}}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E5.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    Q11429
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C10.S1.XMD2.m1ddec
    0 references
    Q11426
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1ddec
    0 references
     
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