DLMF:10.22#Ex4 (Q3376)

From testwiki
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:10.22#Ex4
No description defined

    Statements

    test
    ∫ e i ⁢ z ⁢ z - ν ⁢ 𝒞 ν ⁡ ( z ) ⁢ d z = e i ⁢ z ⁢ z - ν + 1 1 - 2 ⁢ ν ⁢ ( 𝒞 ν ⁡ ( z ) + i ⁢ 𝒞 ν - 1 ⁡ ( z ) ) , superscript 𝑒 𝑖 𝑧 superscript 𝑧 𝜈 cylinder-function 𝜈 𝑧 𝑧 superscript 𝑒 𝑖 𝑧 superscript 𝑧 𝜈 1 1 2 𝜈 cylinder-function 𝜈 𝑧 𝑖 cylinder-function 𝜈 1 𝑧 {\displaystyle{\displaystyle\int e^{iz}z^{-\nu}\mathscr{C}_{\nu}\left(z\right)% \mathrm{d}z=\frac{e^{iz}z^{-\nu+1}}{1-2\nu}(\mathscr{C}_{\nu}\left(z\right)+i% \mathscr{C}_{\nu-1}\left(z\right)),}}
    0 references
    DLMF id
    DLMF:10.22#Ex4
    0 references
    constraint
    ν ≠ 1 2 𝜈 1 2 {\displaystyle{\displaystyle\nu\neq\tfrac{1}{2}}}
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q3376&oldid=17554"