DLMF:4.24.E2 (Q1796): Difference between revisions

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Property / constraint
 

| 1 - z | 2 1 𝑧 2 {\displaystyle{\displaystyle|1-z|\leq 2}}

|1-z|\leq 2
Property / constraint: | 1 - z | 2 1 𝑧 2 {\displaystyle{\displaystyle|1-z|\leq 2}} / rank
 
Normal rank

Revision as of 16:01, 30 December 2019

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DLMF:4.24.E2
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    Statements

    arccos z = ( 2 ( 1 - z ) ) 1 / 2 ( 1 + n = 1 1 3 5 ( 2 n - 1 ) 2 2 n ( 2 n + 1 ) n ! ( 1 - z ) n ) , 𝑧 superscript 2 1 𝑧 1 2 1 superscript subscript 𝑛 1 1 3 5 2 𝑛 1 superscript 2 2 𝑛 2 𝑛 1 𝑛 superscript 1 𝑧 𝑛 {\displaystyle{\displaystyle\operatorname{arccos}z=(2(1-z))^{1/2}\*\left(1+% \sum_{n=1}^{\infty}\frac{1\cdot 3\cdot 5\cdots(2n-1)}{2^{2n}(2n+1)n!}(1-z)^{n}% \right),}}
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    | 1 - z | 2 1 𝑧 2 {\displaystyle{\displaystyle|1-z|\leq 2}}
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