DLMF:9.12.E22 (Q2950): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older edit
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
Property / Symbols used
 
Property / Symbols used: Q11412 / rank
 
Normal rank
Property / Symbols used: Q11412 / qualifier
 
Defining formula:

ζ 𝜁 {\displaystyle{\displaystyle\zeta}}

\zeta
Property / Symbols used: Q11412 / qualifier
 
xml-id: C9.S12.XMD7.m1dec

Latest revision as of 14:55, 2 January 2020

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

    Statements

    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
    DLMF id
    DLMF:9.12.E22
    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)
    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
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aodec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aedec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aedec
    0 references
    modified Bessel function of the second kind
    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
    Q10817
    Defining formula
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1acdec
    0 references
    Q11381
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1rdec
    0 references
    Q11412
    Defining formula
    ζ 𝜁 {\displaystyle{\displaystyle\zeta}}
    xml-id
    C9.S12.XMD7.m1dec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q2950&oldid=52369"