DLMF:9.6.E24 (Q2804): 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.m2amdec
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.m2aadec
Property / Symbols used
 
Property / Symbols used: Whittaker confluent hypergeometric function / rank
 
Normal rank
Property / Symbols used: Whittaker confluent hypergeometric function / qualifier
 
test:

M κ , μ ⁡ ( z ) Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}

\WhittakerconfhyperM{\NVar{\kappa}}{\NVar{\mu}}@{\NVar{z}}
Property / Symbols used: Whittaker confluent hypergeometric function / qualifier
 
xml-id: C13.S14.E2.m2aadec
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.m1wdec
Property / Symbols used
 
Property / Symbols used: change of variable (locally) / rank
 
Normal rank
Property / Symbols used: change of variable (locally) / qualifier
 
test:

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

\zeta
Property / Symbols used: change of variable (locally) / qualifier
 
xml-id: C9.S6.XMD1.m1ldec

Latest revision as of 13:31, 2 January 2020

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DLMF:9.6.E24
No description defined

    Statements

    test
    Bi ′ ⁡ ( z ) = 2 1 / 3 Γ ⁡ ( 1 3 ) ⁢ z 1 / 4 ⁢ M 0 , - 2 / 3 ⁡ ( 2 ⁢ ζ ) + 3 2 10 / 3 ⁢ Γ ⁡ ( 2 3 ) ⁢ z 1 / 4 ⁢ M 0 , 2 / 3 ⁡ ( 2 ⁢ ζ ) , diffop Airy-Bi 1 𝑧 superscript 2 1 3 Euler-Gamma 1 3 superscript 𝑧 1 4 Whittaker-confluent-hypergeometric-M 0 2 3 2 𝜁 3 superscript 2 10 3 Euler-Gamma 2 3 superscript 𝑧 1 4 Whittaker-confluent-hypergeometric-M 0 2 3 2 𝜁 {\displaystyle{\displaystyle\mathrm{Bi}'\left(z\right)=\frac{2^{1/3}}{\Gamma% \left(\tfrac{1}{3}\right)}z^{1/4}M_{0,-2/3}\left(2\zeta\right)+\frac{3}{2^{10/% 3}\Gamma\left(\tfrac{2}{3}\right)}z^{1/4}M_{0,2/3}\left(2\zeta\right),}}
    0 references
    DLMF id
    DLMF:9.6.E24
    0 references
    Symbols used
    Q11081
    test
    Bi ⁡ ( z ) Airy-Bi 𝑧 {\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m2amdec
    0 references
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
    0 references
    Whittaker confluent hypergeometric function
    test
    M κ , μ ⁡ ( z ) Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}
    xml-id
    C13.S14.E2.m2aadec
    0 references
    Q11381
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1wdec
    0 references
    change of variable (locally)
    test
    ζ 𝜁 {\displaystyle{\displaystyle\zeta}}
    xml-id
    C9.S6.XMD1.m1ldec
    0 references
     
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