DLMF:10.5.E5 (Q3028): Difference between revisions

From testwiki
Jump to navigation Jump to search
← Older edit
imported>Admin
imported>Admin
 
(2 intermediate revisions by the same user not shown)
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.m2abdec
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
Property / Symbols used
 
Property / Symbols used: Q11427 / rank
 
Normal rank
Property / Symbols used: Q11427 / qualifier
 
test:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11427 / qualifier
 
xml-id: C10.S1.XMD7.m1ddec

Latest revision as of 15:07, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:10.5.E5
No description defined

    Statements

    test
    𝒲 ⁡ { H ν ( 1 ) ⁡ ( z ) , H ν ( 2 ) ⁡ ( z ) } = H ν + 1 ( 1 ) ⁡ ( z ) ⁢ H ν ( 2 ) ⁡ ( z ) - H ν ( 1 ) ⁡ ( z ) ⁢ H ν + 1 ( 2 ) ⁡ ( z ) = - 4 ⁢ i / ( π ⁢ z ) . Wronskian Hankel-H-1-Bessel-third-kind 𝜈 𝑧 Hankel-H-2-Bessel-third-kind 𝜈 𝑧 Hankel-H-1-Bessel-third-kind 𝜈 1 𝑧 Hankel-H-2-Bessel-third-kind 𝜈 𝑧 Hankel-H-1-Bessel-third-kind 𝜈 𝑧 Hankel-H-2-Bessel-third-kind 𝜈 1 𝑧 4 𝑖 𝜋 𝑧 {\displaystyle{\displaystyle\mathscr{W}\left\{{H^{(1)}_{\nu}}\left(z\right),{H% ^{(2)}_{\nu}}\left(z\right)\right\}={H^{(1)}_{\nu+1}}\left(z\right){H^{(2)}_{% \nu}}\left(z\right)-{H^{(1)}_{\nu}}\left(z\right){H^{(2)}_{\nu+1}}\left(z% \right)=-4i/(\pi z).}}
    0 references
    DLMF id
    DLMF:10.5.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.m2aadec
    0 references
    Bessel function of the third kind (or Hankel function)
    test
    H ν ( 2 ) ⁡ ( z ) Hankel-H-2-Bessel-third-kind 𝜈 𝑧 {\displaystyle{\displaystyle{H^{(2)}_{\NVar{\nu}}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E6.m2aadec
    0 references
    Q10865
    test
    𝒲 Wronskian {\displaystyle{\displaystyle\mathscr{W}}}
    xml-id
    C1.S13.Px2.p1.m3addec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2abdec
    0 references
    Q11426
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1ddec
    0 references
    Q11427
    test
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1ddec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q3028&oldid=15868"