DLMF:14.7.E4 (Q4754): Difference between revisions

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Created a new Item: Wikidata Toolkit example test item creation
 
Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: Q10920 / rank
 
Normal rank
Property / Symbols used: Q10920 / qualifier
 
Defining formula:

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.m2abdec
Property / Symbols used
 
Property / Symbols used: Q11589 / rank
 
Normal rank
Property / Symbols used: Q11589 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11589 / qualifier
 
xml-id: C14.S1.XMD1.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11602 / rank
 
Normal rank
Property / Symbols used: Q11602 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11602 / qualifier
 
xml-id: C14.S1.XMD6.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11603 / rank
 
Normal rank
Property / Symbols used: Q11603 / qualifier
 
Defining formula:

W n - 1 ( x ) subscript 𝑊 𝑛 1 𝑥 {\displaystyle{\displaystyle W_{n-1}(x)}}

W_{n-1}(x)
Property / Symbols used: Q11603 / qualifier
 
xml-id: C14.S7.XMD1.m1bdec

Latest revision as of 01:28, 2 January 2020

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DLMF:14.7.E4
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    Statements

    W n - 1 ( x ) = k = 1 n 1 k P k - 1 ( x ) P n - k ( x ) . subscript 𝑊 𝑛 1 𝑥 superscript subscript 𝑘 1 𝑛 1 𝑘 Legendre-spherical-polynomial 𝑘 1 𝑥 Legendre-spherical-polynomial 𝑛 𝑘 𝑥 {\displaystyle{\displaystyle W_{n-1}(x)=\sum_{k=1}^{n}\frac{1}{k}P_{k-1}\left(% x\right)P_{n-k}\left(x\right).}}
    0 references
    DLMF:14.7.E4
    0 references
    P n ( x ) Legendre-spherical-polynomial 𝑛 𝑥 {\displaystyle{\displaystyle P_{\NVar{n}}\left(\NVar{x}\right)}}
    C18.S3.T1.t1.r10.m2abdec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C14.S1.XMD1.m1cdec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C14.S1.XMD6.m1cdec
    0 references
    W n - 1 ( x ) subscript 𝑊 𝑛 1 𝑥 {\displaystyle{\displaystyle W_{n-1}(x)}}
    C14.S7.XMD1.m1bdec
    0 references