DLMF:18.16.E7 (Q5730): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
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.m2aedec

Revision as of 15:42, 2 January 2020

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DLMF:18.16.E7
No description defined

    Statements

    Defining formula
    θ n , m ≥ j α , m ( ρ 2 + 1 4 - 1 2 ⁢ ( α 2 + β 2 ) - π - 2 ⁢ ( 1 - 4 ⁢ α 2 ) ) 1 2 , subscript 𝜃 𝑛 𝑚 subscript 𝑗 𝛼 𝑚 superscript superscript 𝜌 2 1 4 1 2 superscript 𝛼 2 superscript 𝛽 2 superscript 𝜋 2 1 4 superscript 𝛼 2 1 2 {\displaystyle{\displaystyle\theta_{n,m}\geq\frac{j_{\alpha,m}}{\left(\rho^{2}% +\tfrac{1}{4}-\tfrac{1}{2}(\alpha^{2}+\beta^{2})-\pi^{-2}(1-4\alpha^{2})\right% )^{\frac{1}{2}}},}}
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    DLMF id
    DLMF:18.16.E7
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    comment
    Warning: Falling back to standard tex;
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    constraint
    m = 1 , 2 , … , ⌊ 1 2 ⁢ n ⌋ 𝑚 1 2 … 1 2 𝑛 {\displaystyle{\displaystyle m=1,2,\dots,\left\lfloor\tfrac{1}{2}n\right% \rfloor}}
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    α , β ∈ [ - 1 2 , 1 2 ] 𝛼 𝛽 1 2 1 2 {\displaystyle{\displaystyle\alpha,\beta\in[-\tfrac{1}{2},\tfrac{1}{2}]}}
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    m = 1 , 2 , … , ⌊ 1 2 ⁢ n ⌋ 𝑚 1 2 … 1 2 𝑛 {\displaystyle{\displaystyle m=1,2,\dots,\left\lfloor\tfrac{1}{2}n\right% \rfloor}}
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aedec
    0 references
     
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