DLMF:7.18.E4 (Q2454): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
Property / Symbols used
 
Property / Symbols used: Q11314 / rank
 
Normal rank
Property / Symbols used: Q11314 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11314 / qualifier
 
xml-id: C7.S1.XMD3.m1cdec

Latest revision as of 13:31, 2 January 2020

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DLMF:7.18.E4
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    Statements

    d n d z n ( e z 2 erfc z ) = ( - 1 ) n 2 n n ! e z 2 i n erfc ( z ) , derivative 𝑧 𝑛 superscript 𝑒 superscript 𝑧 2 complementary-error-function 𝑧 superscript 1 𝑛 superscript 2 𝑛 𝑛 superscript 𝑒 superscript 𝑧 2 repeated-integral-complementary-error-function 𝑛 𝑧 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\left(e^% {z^{2}}\operatorname{erfc}z\right)=(-1)^{n}2^{n}n!e^{z^{2}}\mathop{\mathrm{i}^% {n}\mathrm{erfc}}\left(z\right),}}
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    DLMF:7.18.E4
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    n = 0 , 1 , 2 , 𝑛 0 1 2 {\displaystyle{\displaystyle n=0,1,2,\dots}}
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    erfc z complementary-error-function 𝑧 {\displaystyle{\displaystyle\operatorname{erfc}\NVar{z}}}
    C7.S2.E2.m2aadec
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    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    C1.S4.E4.m2aadec
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    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2abdec
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    ! {\displaystyle{\displaystyle!}}
    introduction.Sx4.p1.t1.r15.m5aadec
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    i n erfc ( z ) repeated-integral-complementary-error-function 𝑛 𝑧 {\displaystyle{\displaystyle\mathop{\mathrm{i}^{\NVar{n}}\mathrm{erfc}}\left(% \NVar{z}\right)}}
    C7.S18.E2.m2addec
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    z 𝑧 {\displaystyle{\displaystyle z}}
    C7.S1.XMD2.m1cdec
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    n 𝑛 {\displaystyle{\displaystyle n}}
    C7.S1.XMD3.m1cdec
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