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:9.12.E22 - MaRDI portal

DLMF:9.12.E22 (Q3648)

From MaRDI portal
No description defined
Language Label Description Also known as
English
DLMF:9.12.E22
No description defined

    Statements

    DLMF defining formula
    Hi ⁡ ( - z ) = 4 ⁢ z 2 3 3 / 2 ⁢ π 2 ⁢ ∫ 0 ∞ K 1 / 3 ⁡ ( t ) ζ 2 + t 2 ⁢ d t , Scorer-Hi 𝑧 4 superscript 𝑧 2 superscript 3 3 2 superscript 𝜋 2 superscript subscript 0 modified-Bessel-second-kind 1 3 𝑡 superscript 𝜁 2 superscript 𝑡 2 𝑡 {\displaystyle{\displaystyle\mathrm{Hi}\left(-z\right)=\frac{4z^{2}}{3^{3/2}% \pi^{2}}\int_{0}^{\infty}\frac{K_{1/3}\left(t\right)}{\zeta^{2}+t^{2}}\mathrm{% d}t,}}
    0 references
    constraint
    | ph ⁡ z | < 1 3 ⁢ π phase 𝑧 1 3 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{1}{3}\pi}}
    0 references
    Symbols used
    Scorer function (inhomogeneous Airy function)
    DLMF defining formula
    Hi ⁡ ( z ) Scorer-Hi 𝑧 {\displaystyle{\displaystyle\mathrm{Hi}\left(\NVar{z}\right)}}
    xml-id
    C9.S12.E5.m2andec
    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.m2aodec
    0 references
    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aedec
    0 references
    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aedec
    0 references
    modified Bessel function of the second kind
    DLMF defining formula
    K ν ⁡ ( z ) modified-Bessel-second-kind 𝜈 𝑧 {\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S25.E3.m2adec
    0 references
    phase
    DLMF defining formula
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1acdec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1rdec
    0 references
    variable
    DLMF defining formula
    ζ 𝜁 {\displaystyle{\displaystyle\zeta}}
    xml-id
    C9.S12.XMD7.m1dec
    0 references

    Identifiers

     
    Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Item:Q3648&oldid=24172760"
    Powered by MediaWiki