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

From testwiki
Jump to navigation Jump to search
← Older editNewer edit →
imported>Admin
imported>Admin
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

Revision as of 14:48, 2 January 2020

No description defined
Language Label Description Also known as
English
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
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q3379&oldid=17570"