DLMF:7.18.E5 (Q2455)

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DLMF:7.18.E5
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    Statements

    Defining formula
    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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    DLMF id
    DLMF:7.18.E5
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    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)}}
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    Symbols used
    derivative of $$f$$ with respect to $$x$$
    Defining formula
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2abdec
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    repeated integrals of the complementary error function
    Defining formula
    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.m2aedec
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    Q11312
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C7.S1.XMD2.m1ddec
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