Deprecated: $wgMWOAuthSharedUserIDs=false is deprecated, set $wgMWOAuthSharedUserIDs=true, $wgMWOAuthSharedUserSource='local' instead [Called from MediaWiki\HookContainer\HookContainer::run in /var/www/html/w/includes/HookContainer/HookContainer.php at line 135] in /var/www/html/w/includes/Debug/MWDebug.php on line 372
DLMF:7.5.E6 - MaRDI portal

DLMF:7.5.E6 (Q3050)

From MaRDI portal





No description defined
Language Label Description Also known as
English
DLMF:7.5.E6
No description defined

    Statements

    DLMF defining formula
    e ± 1 2 ⁢ π ⁢ i ⁢ z 2 ⁢ ( g ⁡ ( z ) ± i ⁢ f ⁡ ( z ) ) = 1 2 ⁢ ( 1 ± i ) - ( C ⁡ ( z ) ± i ⁢ S ⁡ ( z ) ) . superscript 𝑒 plus-or-minus 1 2 𝜋 𝑖 superscript 𝑧 2 plus-or-minus Fresnel-auxilliary-function-g 𝑧 𝑖 Fresnel-auxilliary-function-f 𝑧 1 2 plus-or-minus 1 𝑖 plus-or-minus Fresnel-cosine-integral 𝑧 𝑖 Fresnel-sine-integral 𝑧 {\displaystyle{\displaystyle e^{\pm\frac{1}{2}\pi iz^{2}}(\mathrm{g}\left(z% \right)\pm i\mathrm{f}\left(z\right))=\tfrac{1}{2}(1\pm i)-(C\left(z\right)\pm iS% \left(z\right)).}}
    0 references
    Symbols used
    auxiliary function for Fresnel integrals
    DLMF defining formula
    f ⁡ ( z ) Fresnel-auxilliary-function-f 𝑧 {\displaystyle{\displaystyle\mathrm{f}\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E10.m2acdec
    0 references
    auxiliary function for Fresnel integrals
    DLMF defining formula
    g ⁡ ( z ) Fresnel-auxilliary-function-g 𝑧 {\displaystyle{\displaystyle\mathrm{g}\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E11.m2acdec
    0 references
    Fresnel integral
    DLMF defining formula
    C ⁡ ( z ) Fresnel-cosine-integral 𝑧 {\displaystyle{\displaystyle C\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E7.m2abdec
    0 references
    Fresnel integral
    DLMF defining formula
    S ⁡ ( z ) Fresnel-sine-integral 𝑧 {\displaystyle{\displaystyle S\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E8.m2abdec
    0 references
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
    0 references
    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
    0 references
    imaginary unit
    DLMF defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2acdec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C7.S1.XMD2.m1edec
    0 references

    Identifiers

     
    Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Item:Q3050&oldid=24165067"
    Powered by MediaWiki