DLMF:9.12.E18 (Q2946): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11385 / rank
 
Normal rank
Property / Symbols used: Q11385 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11385 / qualifier
 
xml-id: C9.S1.XMD1.m1cdec

Revision as of 14:54, 2 January 2020

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DLMF:9.12.E18
No description defined

    Statements

    Defining formula
    Hi ′ ⁡ ( z ) = 3 - 1 / 3 π ⁢ ∑ k = 0 ∞ Γ ⁡ ( k + 2 3 ) ⁢ ( 3 1 / 3 ⁢ z ) k k ! . diffop Scorer-Hi 1 𝑧 superscript 3 1 3 𝜋 superscript subscript 𝑘 0 Euler-Gamma 𝑘 2 3 superscript superscript 3 1 3 𝑧 𝑘 𝑘 {\displaystyle{\displaystyle\mathrm{Hi}'\left(z\right)=\frac{3^{-1/3}}{\pi}% \sum_{k=0}^{\infty}\Gamma\left(\frac{k+2}{3}\right)\frac{(3^{1/3}z)^{k}}{k!}.}}
    0 references
    DLMF id
    DLMF:9.12.E18
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aedec
    0 references
    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.m2aldec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2akdec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5acdec
    0 references
    Q11385
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C9.S1.XMD1.m1cdec
    0 references
     
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