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

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Property / constraint
 

n = 0 , 1 , 2 , 𝑛 0 1 2 {\displaystyle{\displaystyle n=0,1,2,\dots}}

n=0,1,2,\dots
Property / constraint: n = 0 , 1 , 2 , 𝑛 0 1 2 {\displaystyle{\displaystyle n=0,1,2,\dots}} / rank
 
Normal rank

Revision as of 16:09, 30 December 2019

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DLMF:7.18.E4
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    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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    n = 0 , 1 , 2 , 𝑛 0 1 2 {\displaystyle{\displaystyle n=0,1,2,\dots}}
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