DLMF:10.32.E4 (Q3524)

From testwiki
Revision as of 12:40, 2 January 2020 by imported>Admin (Admin moved page Main Page to Verifying DLMF with Maple and Mathematica)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:10.32.E4
No description defined

    Statements

    test
    I ν ⁡ ( z ) = 1 π ⁢ ∫ 0 π e z ⁢ cos ⁡ θ ⁢ cos ⁡ ( ν ⁢ θ ) ⁢ d θ - sin ⁡ ( ν ⁢ π ) π ⁢ ∫ 0 ∞ e - z ⁢ cosh ⁡ t - ν ⁢ t ⁢ d t , modified-Bessel-first-kind 𝜈 𝑧 1 𝜋 superscript subscript 0 𝜋 superscript 𝑒 𝑧 𝜃 𝜈 𝜃 𝜃 𝜈 𝜋 𝜋 superscript subscript 0 superscript 𝑒 𝑧 𝑡 𝜈 𝑡 𝑡 {\displaystyle{\displaystyle I_{\nu}\left(z\right)=\frac{1}{\pi}\int_{0}^{\pi}% e^{z\cos\theta}\cos\left(\nu\theta\right)\mathrm{d}\theta-\frac{\sin\left(\nu% \pi\right)}{\pi}\int_{0}^{\infty}e^{-z\cosh t-\nu t}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:10.32.E4
    0 references
    constraint
    | ph ⁡ z | < 1 2 ⁢ π phase 𝑧 1 2 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{1}{2}\pi}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q3524&oldid=18705"