DLMF:9.2.E2 (Q2754): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10919 / rank
 
Normal rank
Property / Symbols used: Q10919 / qualifier
 
Defining formula:

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

\AiryAi@{\NVar{z}}
Property / Symbols used: Q10919 / qualifier
 
xml-id: C9.S2.SS1.m1adec
Property / Symbols used
 
Property / Symbols used: Q11081 / rank
 
Normal rank
Property / Symbols used: Q11081 / qualifier
 
Defining formula:

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.m2adec
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
 
Defining formula:

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.m2adec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2adec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
Defining formula:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2adec
Property / Symbols used
 
Property / Symbols used: Q11381 / rank
 
Normal rank
Property / Symbols used: Q11381 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11381 / qualifier
 
xml-id: C9.S1.XMD3.m1adec
Property / Symbols used
 
Property / Symbols used: ODE solution (locally) / rank
 
Normal rank
Property / Symbols used: ODE solution (locally) / qualifier
 
Defining formula:

w 𝑤 {\displaystyle{\displaystyle w}}

w
Property / Symbols used: ODE solution (locally) / qualifier
 
xml-id: C9.S2.XMD1.m1adec

Latest revision as of 14:21, 2 January 2020

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DLMF:9.2.E2
No description defined

    Statements

    Defining formula
    w = Ai ⁡ ( z ) , Bi ⁡ ( z ) , Ai ⁡ ( z ⁢ e ∓ 2 ⁢ π ⁢ i / 3 ) . 𝑤 Airy-Ai 𝑧 Airy-Bi 𝑧 Airy-Ai 𝑧 superscript 𝑒 minus-or-plus 2 𝜋 imaginary-unit 3 {\displaystyle{\displaystyle w=\mathrm{Ai}\left(z\right),\;\mathrm{Bi}\left(z% \right),\;\mathrm{Ai}\left(ze^{\mp 2\pi\mathrm{i}/3}\right).}}
    0 references
    DLMF id
    DLMF:9.2.E2
    0 references
    Symbols used
    Q10919
    Defining formula
    Ai ⁡ ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m1adec
    0 references
    Q11081
    Defining formula
    Bi ⁡ ( z ) Airy-Bi 𝑧 {\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    Q11381
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1adec
    0 references
    ODE solution (locally)
    Defining formula
    w 𝑤 {\displaystyle{\displaystyle w}}
    xml-id
    C9.S2.XMD1.m1adec
    0 references
     
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