DLMF:12.5.E7 (Q4121)

From testwiki
Revision as of 14:10, 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:12.5.E7
No description defined

    Statements

    test
    V ⁡ ( a , z ) = e - 1 4 ⁢ z 2 2 ⁢ π ⁢ ( ∫ - i ⁢ c - ∞ - i ⁢ c + ∞ + ∫ i ⁢ c - ∞ i ⁢ c + ∞ ) ⁢ e z ⁢ t - 1 2 ⁢ t 2 ⁢ t a - 1 2 ⁢ d t , parabolic-V 𝑎 𝑧 superscript 𝑒 1 4 superscript 𝑧 2 2 𝜋 superscript subscript 𝑖 𝑐 𝑖 𝑐 superscript subscript 𝑖 𝑐 𝑖 𝑐 superscript 𝑒 𝑧 𝑡 1 2 superscript 𝑡 2 superscript 𝑡 𝑎 1 2 𝑡 {\displaystyle{\displaystyle V\left(a,z\right)=\frac{e^{-\frac{1}{4}z^{2}}}{2% \pi}\*\left(\int_{-ic-\infty}^{-ic+\infty}+\int_{ic-\infty}^{ic+\infty}\right)% e^{zt-\frac{1}{2}t^{2}}t^{a-\frac{1}{2}}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:12.5.E7
    0 references
    constraint
    - π < ph ⁡ t < π 𝜋 phase 𝑡 𝜋 {\displaystyle{\displaystyle-\pi<\operatorname{ph}{t}<\pi}}
    0 references
    - π < ph ⁡ t < π 𝜋 ph 𝑡 𝜋 {\displaystyle{\displaystyle-\pi<\operatorname{ph}{t}<\pi}}
    0 references
    c > 0 𝑐 0 {\displaystyle{\displaystyle c>0}}
    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.m2aedec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1afdec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q4121&oldid=22197"