DLMF:18.5.E6 (Q5514): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
Defining formula:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5aadec

Revision as of 15:16, 2 January 2020

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DLMF:18.5.E6
No description defined

    Statements

    Defining formula
    L n ( α ) ⁡ ( 1 x ) = ( - 1 ) n n ! ⁢ x n + α + 1 ⁢ e 1 / x ⁢ d n d x n ⁡ ( x - α - 1 ⁢ e - 1 / x ) . Laguerre-polynomial-L 𝛼 𝑛 1 𝑥 superscript 1 𝑛 𝑛 superscript 𝑥 𝑛 𝛼 1 superscript 𝑒 1 𝑥 derivative 𝑥 𝑛 superscript 𝑥 𝛼 1 superscript 𝑒 1 𝑥 {\displaystyle{\displaystyle L^{(\alpha)}_{n}\left(\frac{1}{x}\right)=\frac{(-% 1)^{n}}{n!}x^{n+\alpha+1}e^{\ifrac{1}{x}}\frac{{\mathrm{d}}^{n}}{{\mathrm{d}x}% ^{n}}\left(x^{-\alpha-1}e^{-\ifrac{1}{x}}\right).}}
    0 references
    DLMF id
    DLMF:18.5.E6
    0 references
    Symbols used
    Q11333
    Defining formula
    L n ( α ) ⁡ ( x ) Laguerre-polynomial-L 𝛼 𝑛 𝑥 {\displaystyle{\displaystyle L^{(\NVar{\alpha})}_{\NVar{n}}\left(\NVar{x}% \right)}}
    xml-id
    C18.S3.T1.t1.r12.m2aadec
    0 references
    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.m2aadec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
    0 references
     
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