DLMF:14.7.E13 (Q4765): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10920 / rank
 
Normal rank
Property / Symbols used: Q10920 / qualifier
 
test:

P n ⁡ ( x ) Legendre-spherical-polynomial 𝑛 𝑥 {\displaystyle{\displaystyle P_{\NVar{n}}\left(\NVar{x}\right)}}

\LegendrepolyP{\NVar{n}}@{\NVar{x}}
Property / Symbols used: Q10920 / qualifier
 
xml-id: C18.S3.T1.t1.r10.m2aedec
Property / Symbols used
 
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / rank
 
Normal rank
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / qualifier
 
test:

d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}

\deriv{\NVar{f}}{\NVar{x}}
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / qualifier
 
xml-id: C1.S4.E4.m2aedec
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
test:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5acdec
Property / Symbols used
 
Property / Symbols used: Q11589 / rank
 
Normal rank
Property / Symbols used: Q11589 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11589 / qualifier
 
xml-id: C14.S1.XMD1.m1ldec
Property / Symbols used
 
Property / Symbols used: Q11602 / rank
 
Normal rank
Property / Symbols used: Q11602 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11602 / qualifier
 
xml-id: C14.S1.XMD6.m1kdec

Latest revision as of 00:30, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:14.7.E13
No description defined

    Statements

    test
    P n ⁡ ( x ) = 1 2 n ⁢ n ! ⁢ d n d x n ⁡ ( x 2 - 1 ) n , Legendre-spherical-polynomial 𝑛 𝑥 1 superscript 2 𝑛 𝑛 derivative 𝑥 𝑛 superscript superscript 𝑥 2 1 𝑛 {\displaystyle{\displaystyle P_{n}\left(x\right)=\frac{1}{2^{n}n!}\frac{{% \mathrm{d}}^{n}}{{\mathrm{d}x}^{n}}\left(x^{2}-1\right)^{n},}}
    0 references
    DLMF id
    DLMF:14.7.E13
    0 references
    Symbols used
    Q10920
    test
    P n ⁡ ( x ) Legendre-spherical-polynomial 𝑛 𝑥 {\displaystyle{\displaystyle P_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r10.m2aedec
    0 references
    derivative of $$f$$ with respect to $$x$$
    test
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2aedec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5acdec
    0 references
    Q11589
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1ldec
    0 references
    Q11602
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C14.S1.XMD6.m1kdec
    0 references
     
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