DLMF:10.29.E5 (Q3512): Difference between revisions

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Created a new Item: Wikidata Toolkit example test item creation
 
Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q10754 / rank
 
Normal rank
Property / Symbols used: Q10754 / qualifier
 
Defining formula:

( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}

\binom{\NVar{m}}{\NVar{n}}
Property / Symbols used: Q10754 / qualifier
 
xml-id: C1.S2.SS1.m1adec

Revision as of 13:37, 2 January 2020

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DLMF:10.29.E5
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    Statements

    𝒵 ν ( k ) ( z ) = 1 2 k ( 𝒵 ν - k ( z ) + ( k 1 ) 𝒵 ν - k + 2 ( z ) + ( k 2 ) 𝒵 ν - k + 4 ( z ) + + 𝒵 ν + k ( z ) ) . modified-cylinder-function 𝜈 𝑘 𝑧 1 superscript 2 𝑘 modified-cylinder-function 𝜈 𝑘 𝑧 binomial 𝑘 1 modified-cylinder-function 𝜈 𝑘 2 𝑧 binomial 𝑘 2 modified-cylinder-function 𝜈 𝑘 4 𝑧 modified-cylinder-function 𝜈 𝑘 𝑧 {\displaystyle{\displaystyle{\mathscr{Z}_{\nu}^{(k)}}\left(z\right)=\frac{1}{2% ^{k}}\left(\mathscr{Z}_{\nu-k}\left(z\right)+\genfrac{(}{)}{0.0pt}{}{k}{1}% \mathscr{Z}_{\nu-k+2}\left(z\right)+\genfrac{(}{)}{0.0pt}{}{k}{2}\mathscr{Z}_{% \nu-k+4}\left(z\right)+\cdots+\mathscr{Z}_{\nu+k}\left(z\right)\right).}}
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    DLMF:10.29.E5
    0 references
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    C1.S2.SS1.m1adec
    0 references