DLMF:7.14.E5 (Q2437): 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.m2acdec

Revision as of 00:51, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:7.14.E5
No description defined

    Statements

    test
    ∫ 0 ∞ e - a ⁢ t ⁢ C ⁡ ( t ) ⁢ d t = 1 a ⁢ f ⁡ ( a π ) , superscript subscript 0 superscript 𝑒 𝑎 𝑡 Fresnel-cosine-integral 𝑡 𝑡 1 𝑎 Fresnel-auxilliary-function-f 𝑎 𝜋 {\displaystyle{\displaystyle\int_{0}^{\infty}e^{-at}C\left(t\right)\mathrm{d}t% =\frac{1}{a}\mathrm{f}\left(\frac{a}{\pi}\right),}}
    0 references
    DLMF id
    DLMF:7.14.E5
    0 references
    constraint
    ℜ ⁡ a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}}
    0 references
    Symbols used
    auxiliary function for Fresnel integrals
    test
    f ⁡ ( z ) Fresnel-auxilliary-function-f 𝑧 {\displaystyle{\displaystyle\mathrm{f}\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E10.m2adec
    0 references
    Fresnel integral
    test
    C ⁡ ( z ) Fresnel-cosine-integral 𝑧 {\displaystyle{\displaystyle C\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E7.m2adec
    0 references
    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:Q2437&oldid=12103"