DLMF:9.9.E15 (Q2876): Difference between revisions

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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.m2amdec
Property / Symbols used
 
Property / Symbols used: Q11398 / rank
 
Normal rank
Property / Symbols used: Q11398 / qualifier
 
Defining formula:

β k complex-zero-Airy-Bi 𝑘 {\displaystyle{\displaystyle\beta_{\NVar{k}}}}

\zAirybeta{\NVar{k}}
Property / Symbols used: Q11398 / qualifier
 
xml-id: C9.S9.SS1.p2.m7aadec
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.m2aadec
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.m2aadec
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
Defining formula:

ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2aadec
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.m1ndec
Property / Symbols used
 
Property / Symbols used: expansion (locally) / rank
 
Normal rank
Property / Symbols used: expansion (locally) / qualifier
 
Defining formula:

V 𝑉 {\displaystyle{\displaystyle V}}

V
Property / Symbols used: expansion (locally) / qualifier
 
xml-id: C9.S9.XMD4.m1bdec

Latest revision as of 14:43, 2 January 2020

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DLMF:9.9.E15
No description defined

    Statements

    Defining formula
    Bi ′ ⁡ ( β k ) = ( - 1 ) k ⁢ 2 ⁢ e - π ⁢ i / 6 ⁢ V ⁢ ( 3 8 ⁢ π ⁢ ( 4 ⁢ k - 1 ) + 3 4 ⁢ i ⁢ ln ⁡ 2 ) , diffop Airy-Bi 1 complex-zero-Airy-Bi 𝑘 superscript 1 𝑘 2 superscript 𝑒 𝜋 𝑖 6 𝑉 3 8 𝜋 4 𝑘 1 3 4 𝑖 2 {\displaystyle{\displaystyle\mathrm{Bi}'\left(\beta_{k}\right)=(-1)^{k}\sqrt{2% }e^{-\pi i/6}V\left(\tfrac{3}{8}\pi(4k-1)+\tfrac{3}{4}i\ln 2\right),}}
    0 references
    DLMF id
    DLMF:9.9.E15
    0 references
    Symbols used
    Q11081
    Defining formula
    Bi ⁡ ( z ) Airy-Bi 𝑧 {\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m2addec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2amdec
    0 references
    Q11398
    Defining formula
    β k complex-zero-Airy-Bi 𝑘 {\displaystyle{\displaystyle\beta_{\NVar{k}}}}
    xml-id
    C9.S9.SS1.p2.m7aadec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2aadec
    0 references
    Q11385
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C9.S1.XMD1.m1ndec
    0 references
    expansion (locally)
    Defining formula
    V 𝑉 {\displaystyle{\displaystyle V}}
    xml-id
    C9.S9.XMD4.m1bdec
    0 references
     
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