DLMF:10.22.E6 (Q3379): Difference between revisions

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Property / constraint
 

μ 2 ≠ ν 2 superscript 𝜇 2 superscript 𝜈 2 {\displaystyle{\displaystyle\mu^{2}\neq\nu^{2}}}

\mu^{2}\neq\nu^{2}
Property / constraint: μ 2 ≠ ν 2 superscript 𝜇 2 superscript 𝜈 2 {\displaystyle{\displaystyle\mu^{2}\neq\nu^{2}}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Q11430 / rank
 
Normal rank
Property / Symbols used: Q11430 / qualifier
 
test:

𝒞 ν ⁡ ( z ) cylinder-function 𝜈 𝑧 {\displaystyle{\displaystyle\mathscr{C}_{\NVar{\nu}}\left(\NVar{z}\right)}}

\BesselC{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: Q11430 / qualifier
 
xml-id: C10.S2.Px5.p1.m3aedec
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1aedec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3aedec
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
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.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11439 / rank
 
Normal rank
Property / Symbols used: Q11439 / qualifier
 
test:

𝒟 ν ⁢ ( z ) subscript 𝒟 𝜈 𝑧 {\displaystyle{\displaystyle\mathscr{D}_{\nu}(z)}}

\mathscr{D}_{\nu}(z)
Property / Symbols used: Q11439 / qualifier
 
xml-id: C10.S2.XMD1.m1bdec

Latest revision as of 14:48, 2 January 2020

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DLMF:10.22.E6
No description defined

    Statements

    test
    ∫ 𝒞 μ ⁡ ( a ⁢ z ) ⁢ 𝒟 ν ⁢ ( a ⁢ z ) ⁢ d z z = - a ⁢ z ⁢ ( 𝒞 μ + 1 ⁡ ( a ⁢ z ) ⁢ 𝒟 ν ⁢ ( a ⁢ z ) - 𝒞 μ ⁡ ( a ⁢ z ) ⁢ 𝒟 ν + 1 ⁢ ( a ⁢ z ) ) μ 2 - ν 2 + 𝒞 μ ⁡ ( a ⁢ z ) ⁢ 𝒟 ν ⁢ ( a ⁢ z ) μ + ν , cylinder-function 𝜇 𝑎 𝑧 subscript 𝒟 𝜈 𝑎 𝑧 𝑧 𝑧 𝑎 𝑧 cylinder-function 𝜇 1 𝑎 𝑧 subscript 𝒟 𝜈 𝑎 𝑧 cylinder-function 𝜇 𝑎 𝑧 subscript 𝒟 𝜈 1 𝑎 𝑧 superscript 𝜇 2 superscript 𝜈 2 cylinder-function 𝜇 𝑎 𝑧 subscript 𝒟 𝜈 𝑎 𝑧 𝜇 𝜈 {\displaystyle{\displaystyle\int\mathscr{C}_{\mu}\left(az\right)\mathscr{D}_{% \nu}(az)\frac{\mathrm{d}z}{z}=-\frac{az(\mathscr{C}_{\mu+1}\left(az\right)% \mathscr{D}_{\nu}(az)-\mathscr{C}_{\mu}\left(az\right)\mathscr{D}_{\nu+1}(az))% }{\mu^{2}-\nu^{2}}+\frac{\mathscr{C}_{\mu}\left(az\right)\mathscr{D}_{\nu}(az)% }{\mu+\nu},}}
    0 references
    DLMF id
    DLMF:10.22.E6
    0 references
    constraint
    μ 2 ≠ ν 2 superscript 𝜇 2 superscript 𝜈 2 {\displaystyle{\displaystyle\mu^{2}\neq\nu^{2}}}
    0 references
    Symbols used
    Q11430
    test
    𝒞 ν ⁡ ( z ) cylinder-function 𝜈 𝑧 {\displaystyle{\displaystyle\mathscr{C}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.Px5.p1.m3aedec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aedec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aedec
    0 references
    Q11426
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1edec
    0 references
    Q11427
    test
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1cdec
    0 references
    Q11439
    test
    𝒟 ν ⁢ ( z ) subscript 𝒟 𝜈 𝑧 {\displaystyle{\displaystyle\mathscr{D}_{\nu}(z)}}
    xml-id
    C10.S2.XMD1.m1bdec
    0 references
     
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