DLMF:12.7.E4 (Q4127): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Dawson’s integral / rank
 
Normal rank
Property / Symbols used: Dawson’s integral / qualifier
 
test:

F ( z ) Dawsons-integral 𝑧 {\displaystyle{\displaystyle F\left(\NVar{z}\right)}}

\DawsonsintF@{\NVar{z}}
Property / Symbols used: Dawson’s integral / qualifier
 
xml-id: C7.S2.E5.m2adec
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
 
test:

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.m2aadec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

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: Q11517 / rank
 
Normal rank
Property / Symbols used: Q11517 / qualifier
 
test:

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

\paraV@{\NVar{a}}{\NVar{z}}
Property / Symbols used: Q11517 / qualifier
 
xml-id: C12.S2.SS1.p1.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11513 / rank
 
Normal rank
Property / Symbols used: Q11513 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11513 / qualifier
 
xml-id: C12.S1.XMD3.m1cdec

Latest revision as of 14:12, 2 January 2020

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DLMF:12.7.E4
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    Statements

    V ( - 1 2 , z ) = ( 2 / π ) e 1 4 z 2 F ( z / 2 ) , parabolic-V 1 2 𝑧 2 𝜋 superscript 𝑒 1 4 superscript 𝑧 2 Dawsons-integral 𝑧 2 {\displaystyle{\displaystyle V\left(-\tfrac{1}{2},z\right)=(\ifrac{2}{\sqrt{% \pi}}\,)e^{\frac{1}{4}z^{2}}F\left(z/\sqrt{2}\right),}}
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    F ( z ) Dawsons-integral 𝑧 {\displaystyle{\displaystyle F\left(\NVar{z}\right)}}
    C7.S2.E5.m2adec
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aadec
    0 references
    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2acdec
    0 references
    V ( a , z ) parabolic-V 𝑎 𝑧 {\displaystyle{\displaystyle V\left(\NVar{a},\NVar{z}\right)}}
    C12.S2.SS1.p1.m2aadec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C12.S1.XMD3.m1cdec
    0 references