DLMF:4.40.E9 (Q1981): Difference between revisions

From testwiki
Jump to navigation Jump to search
← Older editNewer edit →
imported>Admin
imported>Admin
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
test:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2abdec

Revision as of 18:22, 1 January 2020

No description defined
Language Label Description Also known as
English
DLMF:4.40.E9
No description defined

    Statements

    test
    ∫ - ∞ ∞ e a ⁢ x ( cosh ⁡ ( 1 2 ⁢ x ) ) 2 ⁢ d x = 4 ⁢ π ⁢ a sin ⁡ ( π ⁢ a ) , superscript subscript superscript 𝑒 𝑎 𝑥 superscript 1 2 𝑥 2 𝑥 4 𝜋 𝑎 𝜋 𝑎 {\displaystyle{\displaystyle\int_{-\infty}^{\infty}\frac{e^{ax}}{\left(\cosh% \left(\tfrac{1}{2}x\right)\right)^{2}}\mathrm{d}x=\frac{4\pi a}{\sin\left(\pi a% \right)},}}
    0 references
    DLMF id
    DLMF:4.40.E9
    0 references
    constraint
    - 1 < a < 1 1 𝑎 1 {\displaystyle{\displaystyle-1<a<1}}
    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.m2abdec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q1981&oldid=9488"