DLMF:9.12.E12 (Q2940): 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: Scorer function (inhomogeneous Airy function) / rank
 
Normal rank
Property / Symbols used: Scorer function (inhomogeneous Airy function) / qualifier
 
Defining formula:

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.m2ahdec
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.m2aedec
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: 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.m1idec

Latest revision as of 14:53, 2 January 2020

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DLMF:9.12.E12
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    Statements

    Gi ( z ) = 1 2 e π i / 3 Hi ( z e - 2 π i / 3 ) + 1 2 e - π i / 3 Hi ( z e 2 π i / 3 ) , Scorer-Gi 𝑧 1 2 superscript 𝑒 𝜋 𝑖 3 Scorer-Hi 𝑧 superscript 𝑒 2 𝜋 𝑖 3 1 2 superscript 𝑒 𝜋 𝑖 3 Scorer-Hi 𝑧 superscript 𝑒 2 𝜋 𝑖 3 {\displaystyle{\displaystyle\mathrm{Gi}\left(z\right)=\tfrac{1}{2}e^{\pi i/3}% \mathrm{Hi}\left(ze^{-2\pi i/3}\right)+\tfrac{1}{2}e^{-\pi i/3}\mathrm{Hi}% \left(ze^{2\pi i/3}\right),}}
    0 references
    DLMF:9.12.E12
    0 references
    Gi ( z ) Scorer-Gi 𝑧 {\displaystyle{\displaystyle\mathrm{Gi}\left(\NVar{z}\right)}}
    C9.S12.E4.m2agdec
    0 references
    Hi ( z ) Scorer-Hi 𝑧 {\displaystyle{\displaystyle\mathrm{Hi}\left(\NVar{z}\right)}}
    C9.S12.E5.m2ahdec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aedec
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    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2acdec
    0 references
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2acdec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C9.S1.XMD3.m1idec
    0 references