DLMF:4.21.E35 (Q1737): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(3 intermediate revisions by the same user not shown)
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.m2avdec
Property / Symbols used
 
Property / Symbols used: Q11219 / rank
 
Normal rank
Property / Symbols used: Q11219 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11219 / qualifier
 
xml-id: C4.S1.XMD1.m1dec
Property / Symbols used
 
Property / Symbols used: Q11223 / rank
 
Normal rank
Property / Symbols used: Q11223 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11223 / qualifier
 
xml-id: C4.S1.XMD3.m1adec
Property / Symbols used
 
Property / Symbols used: Q11217 / rank
 
Normal rank
Property / Symbols used: Q11217 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11217 / qualifier
 
xml-id: C4.S1.XMD8.m1qdec

Latest revision as of 18:27, 1 January 2020

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DLMF:4.21.E35
No description defined

    Statements

    sin ( n z ) = 2 n - 1 k = 0 n - 1 sin ( z + k π n ) , 𝑛 𝑧 superscript 2 𝑛 1 superscript subscript product 𝑘 0 𝑛 1 𝑧 𝑘 𝜋 𝑛 {\displaystyle{\displaystyle\sin\left(nz\right)=2^{n-1}\prod_{k=0}^{n-1}\sin% \left(z+\frac{k\pi}{n}\right),}}
    0 references
    DLMF:4.21.E35
    0 references
    n = 1 , 2 , 3 , 𝑛 1 2 3 {\displaystyle{\displaystyle n=1,2,3,\dots}}
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aadec
    0 references
    sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    C4.S14.E1.m2avdec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C4.S1.XMD1.m1dec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C4.S1.XMD3.m1adec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C4.S1.XMD8.m1qdec
    0 references