DLMF:9.12.E26 (Q2954): Difference between revisions

From testwiki
Jump to navigation Jump to search
imported>Admin
 
imported>Admin
 
(8 intermediate revisions by the same user not shown)
Property / constraint
 

| ph ⁡ z | ≤ 1 3 ⁢ π - δ phase 𝑧 1 3 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{1}{3}\pi-\delta}}

|\phase@@{z}|\leq\tfrac{1}{3}\pi-\delta
Property / constraint: | ph ⁡ z | ≤ 1 3 ⁢ π - δ phase 𝑧 1 3 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{1}{3}\pi-\delta}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Scorer function (inhomogeneous Airy function) / rank
 
Normal rank
Property / Symbols used: Scorer function (inhomogeneous Airy function) / qualifier
 
test:

Gi ⁡ ( z ) Scorer-Gi 𝑧 {\displaystyle{\displaystyle\mathrm{Gi}\left(\NVar{z}\right)}}

\ScorerGi@{\NVar{z}}
Property / Symbols used: Scorer function (inhomogeneous Airy function) / qualifier
 
xml-id: C9.S12.E4.m2aodec
Property / Symbols used
 
Property / Symbols used: Q10931 / rank
 
Normal rank
Property / Symbols used: Q10931 / qualifier
 
test:

∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}

\asympexp
Property / Symbols used: Q10931 / qualifier
 
xml-id: C2.S1.SS3.p1.m11aadec
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.m2asdec
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
test:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5aedec
Property / Symbols used
 
Property / Symbols used: Q10817 / rank
 
Normal rank
Property / Symbols used: Q10817 / qualifier
 
test:

ph phase {\displaystyle{\displaystyle\operatorname{ph}}}

\phase
Property / Symbols used: Q10817 / qualifier
 
xml-id: C1.S9.E7.m1aedec
Property / Symbols used
 
Property / Symbols used: Q11385 / rank
 
Normal rank
Property / Symbols used: Q11385 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11385 / qualifier
 
xml-id: C9.S1.XMD1.m1edec
Property / Symbols used
 
Property / Symbols used: Q11381 / rank
 
Normal rank
Property / Symbols used: Q11381 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11381 / qualifier
 
xml-id: C9.S1.XMD3.m1udec
Property / Symbols used
 
Property / Symbols used: Q11386 / rank
 
Normal rank
Property / Symbols used: Q11386 / qualifier
 
test:

δ 𝛿 {\displaystyle{\displaystyle\delta}}

\delta
Property / Symbols used: Q11386 / qualifier
 
xml-id: C9.S1.XMD4.m1adec

Latest revision as of 13:56, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:9.12.E26
No description defined

    Statements

    test
    Gi ′ ⁡ ( z ) ∼ - 1 π ⁢ z 2 ⁢ ∑ k = 0 ∞ ( 3 ⁢ k + 1 ) ! k ! ⁢ ( 3 ⁢ z 3 ) k , asymptotic-expansion diffop Scorer-Gi 1 𝑧 1 𝜋 superscript 𝑧 2 superscript subscript 𝑘 0 3 𝑘 1 𝑘 superscript 3 superscript 𝑧 3 𝑘 {\displaystyle{\displaystyle\mathrm{Gi}'\left(z\right)\sim-\frac{1}{\pi z^{2}}% \sum_{k=0}^{\infty}\frac{(3k+1)!}{k!(3z^{3})^{k}},}}
    0 references
    DLMF id
    DLMF:9.12.E26
    0 references
    constraint
    | ph ⁡ z | ≤ 1 3 ⁢ π - δ phase 𝑧 1 3 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{1}{3}\pi-\delta}}
    0 references
    Symbols used
    Scorer function (inhomogeneous Airy function)
    test
    Gi ⁡ ( z ) Scorer-Gi 𝑧 {\displaystyle{\displaystyle\mathrm{Gi}\left(\NVar{z}\right)}}
    xml-id
    C9.S12.E4.m2aodec
    0 references
    Q10931
    test
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2asdec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aedec
    0 references
    Q10817
    test
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1aedec
    0 references
    Q11385
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C9.S1.XMD1.m1edec
    0 references
    Q11381
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1udec
    0 references
    Q11386
    test
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C9.S1.XMD4.m1adec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q2954&oldid=15434"