DLMF:4.24.E5 (Q1799): Difference between revisions

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Created a new Item: Wikidata Toolkit example test item creation
 
Changed an Item: Add constraint
Property / constraint
 

( z 2 ) > - 1 2 superscript 𝑧 2 1 2 {\displaystyle{\displaystyle\Re(z^{2})>-\tfrac{1}{2}}}

\realpart@@{(z^{2})}>-\tfrac{1}{2}
Property / constraint: ( z 2 ) > - 1 2 superscript 𝑧 2 1 2 {\displaystyle{\displaystyle\Re(z^{2})>-\tfrac{1}{2}}} / rank
 
Normal rank

Revision as of 17:01, 30 December 2019

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DLMF:4.24.E5
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    Statements

    arctan z = z z 2 + 1 ( 1 + 2 3 z 2 1 + z 2 + 2 4 3 5 ( z 2 1 + z 2 ) 2 + ) , 𝑧 𝑧 superscript 𝑧 2 1 1 2 3 superscript 𝑧 2 1 superscript 𝑧 2 2 4 3 5 superscript superscript 𝑧 2 1 superscript 𝑧 2 2 {\displaystyle{\displaystyle\operatorname{arctan}z=\frac{z}{z^{2}+1}\*\left(1+% \frac{2}{3}\frac{z^{2}}{1+z^{2}}+\frac{2\cdot 4}{3\cdot 5}\left(\frac{z^{2}}{1% +z^{2}}\right)^{2}+\cdots\right),}}
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    DLMF:4.24.E5
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    ( z 2 ) > - 1 2 superscript 𝑧 2 1 2 {\displaystyle{\displaystyle\Re(z^{2})>-\tfrac{1}{2}}}
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