DLMF:12.5.E6 (Q4120): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11320 / rank
 
Normal rank
Property / Symbols used: Q11320 / qualifier
 
Defining formula:

U ( a , z ) parabolic-U 𝑎 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}

\paraU@{\NVar{a}}{\NVar{z}}
Property / Symbols used: Q11320 / qualifier
 
xml-id: C12.S2.SS1.p1.m1aedec

Revision as of 15:10, 2 January 2020

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DLMF:12.5.E6
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    Statements

    U ( a , z ) = e 1 4 z 2 i 2 π c - i c + i e - z t + 1 2 t 2 t - a - 1 2 d t , parabolic-U 𝑎 𝑧 superscript 𝑒 1 4 superscript 𝑧 2 𝑖 2 𝜋 superscript subscript 𝑐 𝑖 𝑐 𝑖 superscript 𝑒 𝑧 𝑡 1 2 superscript 𝑡 2 superscript 𝑡 𝑎 1 2 𝑡 {\displaystyle{\displaystyle U\left(a,z\right)=\frac{e^{\frac{1}{4}z^{2}}}{i% \sqrt{2\pi}}\int_{c-i\infty}^{c+i\infty}e^{-zt+\frac{1}{2}t^{2}}t^{-a-\frac{1}% {2}}\mathrm{d}t,}}
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    DLMF:12.5.E6
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    - 1 2 π < ph t < 1 2 π 1 2 𝜋 phase 𝑡 1 2 𝜋 {\displaystyle{\displaystyle-\tfrac{1}{2}\pi<\operatorname{ph}t<\tfrac{1}{2}% \pi}}
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    - 1 2 π < ph t < 1 2 π 1 2 𝜋 ph 𝑡 1 2 𝜋 {\displaystyle{\displaystyle-\tfrac{1}{2}\pi<\operatorname{ph}t<\tfrac{1}{2}% \pi}}
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    c > 0 𝑐 0 {\displaystyle{\displaystyle c>0}}
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2addec
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    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1aedec
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    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2aedec
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    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2aadec
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    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3aedec
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    U ( a , z ) parabolic-U 𝑎 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}
    C12.S2.SS1.p1.m1aedec
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