DLMF:36.7.E8 (Q9942): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2afdec
Property / Symbols used
 
Property / Symbols used: sine function / rank
 
Normal rank
Property / Symbols used: sine function / qualifier
 
Defining formula:

sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2adec
Property / Symbols used
 
Property / Symbols used: Q12755 / rank
 
Normal rank
Property / Symbols used: Q12755 / qualifier
 
Defining formula:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q12755 / qualifier
 
xml-id: C36.S1.XMD3.m1gdec

Latest revision as of 15:10, 2 January 2020

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DLMF:36.7.E8
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    Statements

    r = 3 ( ( 2 n - 1 ) π 4 | sin ( 3 2 θ ) | ) 2 / 3 ( 1 + O ( n - 1 ) ) , 𝑟 3 superscript 2 𝑛 1 𝜋 4 3 2 𝜃 2 3 1 Big-O superscript 𝑛 1 {\displaystyle{\displaystyle r=3\left(\frac{(2n-1)\pi}{4|\sin\left(\tfrac{3}{2% }\theta\right)|}\right)^{2/3}(1+O\left(n^{-1}\right)),}}
    0 references
    DLMF:36.7.E8
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    n 𝑛 {\displaystyle{\displaystyle n\to\infty}}
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    O ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    C2.S1.E3.m2adec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2afdec
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    sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    C4.S14.E1.m2adec
    0 references
    m 𝑚 {\displaystyle{\displaystyle m}}
    C36.S1.XMD3.m1gdec
    0 references