DLMF:27.7.E6 (Q8046): 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 / constraint
 

| x | < 1 𝑥 1 {\displaystyle{\displaystyle|x|<1}}

|x|<1
Property / constraint: | x | < 1 𝑥 1 {\displaystyle{\displaystyle|x|<1}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Liouville’s function / rank
 
Normal rank
Property / Symbols used: Liouville’s function / qualifier
 
Defining formula:

λ ( n ) Liouville-lambda 𝑛 {\displaystyle{\displaystyle\lambda\left(\NVar{n}\right)}}

\Liouvillelambda@{\NVar{n}}
Property / Symbols used: Liouville’s function / qualifier
 
xml-id: C27.S2.E13.m2adec
Property / Symbols used
 
Property / Symbols used: Q12234 / rank
 
Normal rank
Property / Symbols used: Q12234 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12234 / qualifier
 
xml-id: C27.S1.XMD4.m1edec
Property / Symbols used
 
Property / Symbols used: Q12237 / rank
 
Normal rank
Property / Symbols used: Q12237 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q12237 / qualifier
 
xml-id: C27.S1.XMD6.m1edec

Latest revision as of 14:20, 2 January 2020

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DLMF:27.7.E6
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    Statements

    n = 1 λ ( n ) x n 1 - x n = n = 1 x n 2 . superscript subscript 𝑛 1 Liouville-lambda 𝑛 superscript 𝑥 𝑛 1 superscript 𝑥 𝑛 superscript subscript 𝑛 1 superscript 𝑥 superscript 𝑛 2 {\displaystyle{\displaystyle\sum_{n=1}^{\infty}\lambda\left(n\right)\frac{x^{n% }}{1-x^{n}}=\sum_{n=1}^{\infty}x^{n^{2}}.}}
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    DLMF:27.7.E6
    0 references
    | x | < 1 𝑥 1 {\displaystyle{\displaystyle|x|<1}}
    0 references
    λ ( n ) Liouville-lambda 𝑛 {\displaystyle{\displaystyle\lambda\left(\NVar{n}\right)}}
    C27.S2.E13.m2adec
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    n 𝑛 {\displaystyle{\displaystyle n}}
    C27.S1.XMD4.m1edec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C27.S1.XMD6.m1edec
    0 references