DLMF:9.12.E6 (Q2934): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11081 / rank
 
Normal rank
Property / Symbols used: Q11081 / qualifier
 
test:

Bi ⁡ ( z ) Airy-Bi 𝑧 {\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}

\AiryBi@{\NVar{z}}
Property / Symbols used: Q11081 / qualifier
 
xml-id: C9.S2.SS1.m2abdec
Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
test:

Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

\EulerGamma@{\NVar{z}}
Property / Symbols used: gamma function / qualifier
 
xml-id: C5.S2.E1.m2adec
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.m2acdec
Property / Symbols used
 
Property / Symbols used: Scorer function (inhomogeneous Airy function) / rank
 
Normal rank
Property / Symbols used: Scorer function (inhomogeneous Airy function) / qualifier
 
test:

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

\ScorerHi@{\NVar{z}}
Property / Symbols used: Scorer function (inhomogeneous Airy function) / qualifier
 
xml-id: C9.S12.E5.m2acdec

Latest revision as of 13:52, 2 January 2020

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DLMF:9.12.E6
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    Statements

    test
    Gi ⁡ ( 0 ) = 1 2 ⁢ Hi ⁡ ( 0 ) = 1 3 ⁢ Bi ⁡ ( 0 ) = 1 / ( 3 7 / 6 ⁢ Γ ⁡ ( 2 3 ) ) = 0.20497 55424 ⁢ … , Scorer-Gi 0 1 2 Scorer-Hi 0 1 3 Airy-Bi 0 1 superscript 3 7 6 Euler-Gamma 2 3 0.20497 55424 … {\displaystyle{\displaystyle\mathrm{Gi}\left(0\right)=\tfrac{1}{2}\mathrm{Hi}% \left(0\right)=\tfrac{1}{3}\mathrm{Bi}\left(0\right)={1\Big{/}\!\left(3^{7/6}% \Gamma\left(\tfrac{2}{3}\right)\right)=0.20497\;55424\ldots,}}}
    0 references
    DLMF id
    DLMF:9.12.E6
    0 references
    Symbols used
    Q11081
    test
    Bi ⁡ ( z ) Airy-Bi 𝑧 {\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m2abdec
    0 references
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    0 references
    Scorer function (inhomogeneous Airy function)
    test
    Gi ⁡ ( z ) Scorer-Gi 𝑧 {\displaystyle{\displaystyle\mathrm{Gi}\left(\NVar{z}\right)}}
    xml-id
    C9.S12.E4.m2acdec
    0 references
    Scorer function (inhomogeneous Airy function)
    test
    Hi ⁡ ( z ) Scorer-Hi 𝑧 {\displaystyle{\displaystyle\mathrm{Hi}\left(\NVar{z}\right)}}
    xml-id
    C9.S12.E5.m2acdec
    0 references
     
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