DLMF:18.17.E44 (Q5785): Difference between revisions

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Property / constraint
 

- 1 ≤ x ≤ 1 1 𝑥 1 {\displaystyle{\displaystyle-1\leq x\leq 1}}

-1\leq x\leq 1
Property / constraint: - 1 ≤ x ≤ 1 1 𝑥 1 {\displaystyle{\displaystyle-1\leq x\leq 1}} / rank
 
Normal rank
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.m2agdec
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1aaqdec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3aaodec
Property / Symbols used
 
Property / Symbols used: Q11726 / rank
 
Normal rank
Property / Symbols used: Q11726 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11726 / qualifier
 
xml-id: C18.S1.XMD6.m1aqdec
Property / Symbols used
 
Property / Symbols used: Q11727 / rank
 
Normal rank
Property / Symbols used: Q11727 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11727 / qualifier
 
xml-id: C18.S2.XMD3.m1aodec

Latest revision as of 00:20, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:18.17.E44
No description defined

    Statements

    test
    ∫ - 1 1 P n ⁡ ( x ) - P n ⁡ ( t ) | x - t | ⁢ d t = 2 ⁢ ( 1 + 1 2 + … + 1 n ) ⁢ P n ⁡ ( x ) , superscript subscript 1 1 Legendre-spherical-polynomial 𝑛 𝑥 Legendre-spherical-polynomial 𝑛 𝑡 𝑥 𝑡 𝑡 2 1 1 2 … 1 𝑛 Legendre-spherical-polynomial 𝑛 𝑥 {\displaystyle{\displaystyle\int_{-1}^{1}\frac{P_{n}\left(x\right)-P_{n}\left(% t\right)}{|x-t|}\mathrm{d}t=2\left(1+\tfrac{1}{2}+\dots+\tfrac{1}{n}\right)P_{% n}\left(x\right),}}
    0 references
    DLMF id
    DLMF:18.17.E44
    0 references
    constraint
    - 1 ≤ x ≤ 1 1 𝑥 1 {\displaystyle{\displaystyle-1\leq x\leq 1}}
    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.m2agdec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aaqdec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aaodec
    0 references
    Q11726
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1aqdec
    0 references
    Q11727
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1aodec
    0 references
     
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