DLMF:9.9.E17 (Q2878): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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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.m2aodec
Property / Symbols used
 
Property / Symbols used: Q11399 / rank
 
Normal rank
Property / Symbols used: Q11399 / qualifier
 
Defining formula:

β k complex-zero-derivative-Airy-Bi 𝑘 {\displaystyle{\displaystyle\beta^{\prime}_{\NVar{k}}}}

\zderivAirybeta{\NVar{k}}
Property / Symbols used: Q11399 / qualifier
 
xml-id: C9.S9.SS1.p2.m10aadec
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.m2acdec
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.m2acdec
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.m2acdec
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.m1pdec
Property / Symbols used
 
Property / Symbols used: expansion (locally) / rank
 
Normal rank
Property / Symbols used: expansion (locally) / qualifier
 
Defining formula:

W 𝑊 {\displaystyle{\displaystyle W}}

W
Property / Symbols used: expansion (locally) / qualifier
 
xml-id: C9.S9.XMD5.m1bdec

Latest revision as of 14:43, 2 January 2020

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DLMF:9.9.E17
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    Statements

    Bi ( β k ) = ( - 1 ) k - 1 2 e π i / 6 W ( 3 8 π ( 4 k - 3 ) + 3 4 i ln 2 ) . Airy-Bi complex-zero-derivative-Airy-Bi 𝑘 superscript 1 𝑘 1 2 superscript 𝑒 𝜋 𝑖 6 𝑊 3 8 𝜋 4 𝑘 3 3 4 𝑖 2 {\displaystyle{\displaystyle\mathrm{Bi}\left(\beta^{\prime}_{k}\right)=(-1)^{k% -1}\sqrt{2}e^{\pi i/6}W\left(\tfrac{3}{8}\pi(4k-3)+\tfrac{3}{4}i\ln 2\right).}}
    0 references
    DLMF:9.9.E17
    0 references
    Bi ( z ) Airy-Bi 𝑧 {\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}
    C9.S2.SS1.m2aedec
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aodec
    0 references
    β k complex-zero-derivative-Airy-Bi 𝑘 {\displaystyle{\displaystyle\beta^{\prime}_{\NVar{k}}}}
    C9.S9.SS1.p2.m10aadec
    0 references
    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2acdec
    0 references
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2acdec
    0 references
    ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    C4.S2.E2.m2acdec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C9.S1.XMD1.m1pdec
    0 references
    W 𝑊 {\displaystyle{\displaystyle W}}
    C9.S9.XMD5.m1bdec
    0 references