DLMF:7.18.E5 (Q2455): Difference between revisions

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Property / constraint
 

W ( z ) = A i n erfc ( z ) + B i n erfc ( - z ) 𝑊 𝑧 𝐴 repeated-integral-complementary-error-function 𝑛 𝑧 𝐵 repeated-integral-complementary-error-function 𝑛 𝑧 {\displaystyle{\displaystyle W(z)=A\mathop{\mathrm{i}^{n}\mathrm{erfc}}\left(z% \right)+B\mathop{\mathrm{i}^{n}\mathrm{erfc}}\left(-z\right)}}

W(z)=A\repinterfc{n}@{z}+B\repinterfc{n}@{-z}
Property / constraint: W ( z ) = A i n erfc ( z ) + B i n erfc ( - z ) 𝑊 𝑧 𝐴 repeated-integral-complementary-error-function 𝑛 𝑧 𝐵 repeated-integral-complementary-error-function 𝑛 𝑧 {\displaystyle{\displaystyle W(z)=A\mathop{\mathrm{i}^{n}\mathrm{erfc}}\left(z% \right)+B\mathop{\mathrm{i}^{n}\mathrm{erfc}}\left(-z\right)}} / rank
 
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Revision as of 16:09, 30 December 2019

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DLMF:7.18.E5
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    Statements

    d 2 W d z 2 + 2 z d W d z - 2 n W = 0 , derivative 𝑊 𝑧 2 2 𝑧 derivative 𝑊 𝑧 2 𝑛 𝑊 0 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}W}{{\mathrm{d}z}^{2}}+2z% \frac{\mathrm{d}W}{\mathrm{d}z}-2nW=0,}}
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    W ( z ) = A i n erfc ( z ) + B i n erfc ( - z ) 𝑊 𝑧 𝐴 repeated-integral-complementary-error-function 𝑛 𝑧 𝐵 repeated-integral-complementary-error-function 𝑛 𝑧 {\displaystyle{\displaystyle W(z)=A\mathop{\mathrm{i}^{n}\mathrm{erfc}}\left(z% \right)+B\mathop{\mathrm{i}^{n}\mathrm{erfc}}\left(-z\right)}}
    0 references