DLMF:7.18.E7 (Q2457): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: repeated integrals of the complementary error function / rank
 
Normal rank
Property / Symbols used: repeated integrals of the complementary error function / qualifier
 
test:

i n ⁢ erfc ⁡ ( z ) repeated-integral-complementary-error-function 𝑛 𝑧 {\displaystyle{\displaystyle\mathop{\mathrm{i}^{\NVar{n}}\mathrm{erfc}}\left(% \NVar{z}\right)}}

\repinterfc{\NVar{n}}@{\NVar{z}}
Property / Symbols used: repeated integrals of the complementary error function / qualifier
 
xml-id: C7.S18.E2.m2agdec

Revision as of 12:32, 2 January 2020

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DLMF:7.18.E7
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    Statements

    test
    i n ⁢ erfc ⁡ ( z ) = - z n ⁢ i n - 1 ⁢ erfc ⁡ ( z ) + 1 2 ⁢ n ⁢ i n - 2 ⁢ erfc ⁡ ( z ) , repeated-integral-complementary-error-function 𝑛 𝑧 𝑧 𝑛 repeated-integral-complementary-error-function 𝑛 1 𝑧 1 2 𝑛 repeated-integral-complementary-error-function 𝑛 2 𝑧 {\displaystyle{\displaystyle\mathop{\mathrm{i}^{n}\mathrm{erfc}}\left(z\right)% =-\frac{z}{n}\mathop{\mathrm{i}^{n-1}\mathrm{erfc}}\left(z\right)+\frac{1}{2n}% \mathop{\mathrm{i}^{n-2}\mathrm{erfc}}\left(z\right),}}
    0 references
    DLMF id
    DLMF:7.18.E7
    0 references
    constraint
    n = 1 , 2 , 3 , … 𝑛 1 2 3 … {\displaystyle{\displaystyle n=1,2,3,\dots}}
    0 references
    Symbols used
    repeated integrals of the complementary error function
    test
    i n ⁢ erfc ⁡ ( z ) repeated-integral-complementary-error-function 𝑛 𝑧 {\displaystyle{\displaystyle\mathop{\mathrm{i}^{\NVar{n}}\mathrm{erfc}}\left(% \NVar{z}\right)}}
    xml-id
    C7.S18.E2.m2agdec
    0 references
     
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