DLMF:7.10.E1 (Q2398): Difference between revisions

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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.m1dec

Latest revision as of 01:48, 2 January 2020

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DLMF:7.10.E1
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    Statements

    Defining formula
    d n + 1 erf ⁡ z d z n + 1 = ( - 1 ) n ⁢ 2 π ⁢ H n ⁡ ( z ) ⁢ e - z 2 , derivative error-function 𝑧 𝑧 𝑛 1 superscript 1 𝑛 2 𝜋 Hermite-polynomial-H 𝑛 𝑧 superscript 𝑒 superscript 𝑧 2 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n+1}\operatorname{erf}z}{{% \mathrm{d}z}^{n+1}}=(-1)^{n}\frac{2}{\sqrt{\pi}}H_{n}\left(z\right)e^{-z^{2}},}}
    0 references
    DLMF id
    DLMF:7.10.E1
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    constraint
    n = 0 , 1 , 2 , … 𝑛 0 1 2 … {\displaystyle{\displaystyle n=0,1,2,\dots}}
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    Symbols used
    Q10922
    Defining formula
    H n ⁡ ( x ) Hermite-polynomial-H 𝑛 𝑥 {\displaystyle{\displaystyle H_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r13.m2adec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    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.m2adec
    0 references
    error function
    Defining formula
    erf ⁡ z error-function 𝑧 {\displaystyle{\displaystyle\operatorname{erf}\NVar{z}}}
    xml-id
    C7.S2.E1.m2adec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    Q11312
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C7.S1.XMD2.m1dec
    0 references
    Q11314
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C7.S1.XMD3.m1dec
    0 references
     
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