DLMF:3.5.E16 (Q1254): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11169 / rank
 
Normal rank
Property / Symbols used: Q11169 / qualifier
 
Defining formula:

⌊ x ⌋ 𝑥 {\displaystyle{\displaystyle\left\lfloor\NVar{x}\right\rfloor}}

\floor{\NVar{x}}
Property / Symbols used: Q11169 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r17.m4adec
Property / Symbols used
 
Property / Symbols used: Q11168 / rank
 
Normal rank
Property / Symbols used: Q11168 / qualifier
 
Defining formula:

w k subscript 𝑤 𝑘 {\displaystyle{\displaystyle w_{k}}}

w_{k}
Property / Symbols used: Q11168 / qualifier
 
xml-id: C3.S5.XMD6.m1adec
Property / Symbols used
 
Property / Symbols used: coefficient (locally) / rank
 
Normal rank
Property / Symbols used: coefficient (locally) / qualifier
 
Defining formula:

g k subscript 𝑔 𝑘 {\displaystyle{\displaystyle g_{k}}}

g_{k}
Property / Symbols used: coefficient (locally) / qualifier
 
xml-id: C3.S5.XMD7.m1dec
Property / Symbols used
 
Property / Symbols used: coefficient (locally) / rank
 
Normal rank
Property / Symbols used: coefficient (locally) / qualifier
 
Defining formula:

b k subscript 𝑏 𝑘 {\displaystyle{\displaystyle b_{k}}}

b_{k}
Property / Symbols used: coefficient (locally) / qualifier
 
xml-id: C3.S5.XMD8.m1dec

Latest revision as of 17:50, 1 January 2020

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DLMF:3.5.E16
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    Statements

    Defining formula
    w k = g k n ⁢ ( 1 - ∑ j = 1 ⌊ n / 2 ⌋ b j 4 ⁢ j 2 - 1 ⁢ cos ⁡ ( 2 ⁢ j ⁢ k ⁢ π / n ) ) , subscript 𝑤 𝑘 subscript 𝑔 𝑘 𝑛 1 superscript subscript 𝑗 1 𝑛 2 subscript 𝑏 𝑗 4 superscript 𝑗 2 1 2 𝑗 𝑘 𝑛 {\displaystyle{\displaystyle w_{k}=\frac{g_{k}}{n}\left(1-\sum_{j=1}^{\left% \lfloor n/2\right\rfloor}\frac{b_{j}}{4j^{2}-1}\cos\left(2jk\pi/n\right)\right% ),}}
    0 references
    DLMF id
    DLMF:3.5.E16
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2adec
    0 references
    Q11169
    Defining formula
    ⌊ x ⌋ 𝑥 {\displaystyle{\displaystyle\left\lfloor\NVar{x}\right\rfloor}}
    xml-id
    introduction.Sx4.p1.t1.r17.m4adec
    0 references
    Q11168
    Defining formula
    w k subscript 𝑤 𝑘 {\displaystyle{\displaystyle w_{k}}}
    xml-id
    C3.S5.XMD6.m1adec
    0 references
    coefficient (locally)
    Defining formula
    g k subscript 𝑔 𝑘 {\displaystyle{\displaystyle g_{k}}}
    xml-id
    C3.S5.XMD7.m1dec
    0 references
    coefficient (locally)
    Defining formula
    b k subscript 𝑏 𝑘 {\displaystyle{\displaystyle b_{k}}}
    xml-id
    C3.S5.XMD8.m1dec
    0 references
     
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