DLMF:8.21.E2 (Q2723): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
Property / Symbols used
 
Property / Symbols used: Q11324 / rank
 
Normal rank
Property / Symbols used: Q11324 / qualifier
 
Defining formula:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q11324 / qualifier
 
xml-id: C8.S1.XMD3.m1adec

Latest revision as of 14:15, 2 January 2020

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DLMF:8.21.E2
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    Statements

    Ci ( a , z ) ± i Si ( a , z ) = e ± 1 2 π i a γ ( a , z e 1 2 π i ) . plus-or-minus generalized-cosine-integral-Ci 𝑎 𝑧 𝑖 generalized-sine-integral-Si 𝑎 𝑧 superscript 𝑒 plus-or-minus 1 2 𝜋 𝑖 𝑎 incomplete-gamma 𝑎 𝑧 superscript 𝑒 minus-or-plus 1 2 𝜋 𝑖 {\displaystyle{\displaystyle\mathrm{Ci}\left(a,z\right)\pm i\mathrm{Si}\left(a% ,z\right)=e^{\pm\frac{1}{2}\pi ia}\gamma\left(a,ze^{\mp\frac{1}{2}\pi i}\right% ).}}
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    DLMF:8.21.E2
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aadec
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    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2aadec
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    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2aadec
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    γ ( a , z ) incomplete-gamma 𝑎 𝑧 {\displaystyle{\displaystyle\gamma\left(\NVar{a},\NVar{z}\right)}}
    C8.S2.E1.m2adec
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    z 𝑧 {\displaystyle{\displaystyle z}}
    C8.S1.XMD2.m1adec
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    a 𝑎 {\displaystyle{\displaystyle a}}
    C8.S1.XMD3.m1adec
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