DLMF:1.8.E8 (Q262): Difference between revisions

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Property / Symbols defined
 
Property / Symbols defined: Lebesgue constants (locally) / rank
 
Normal rank
Property / constraint
 

n = 0 , 1 , 𝑛 0 1 {\displaystyle{\displaystyle n=0,1,\dots}}

n=0,1,\dots
Property / constraint: n = 0 , 1 , 𝑛 0 1 {\displaystyle{\displaystyle n=0,1,\dots}} / rank
 
Normal rank
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
 
test:

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.m2addec
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1addec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

{\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3addec
Property / Symbols used
 
Property / Symbols used: sine function / rank
 
Normal rank
Property / Symbols used: sine function / qualifier
 
test:

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

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2abdec
Property / Symbols used
 
Property / Symbols used: Q10757 / rank
 
Normal rank
Property / Symbols used: Q10757 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q10757 / qualifier
 
xml-id: C1.S1.XMD7.m1gdec

Latest revision as of 15:04, 1 January 2020

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DLMF:1.8.E8
No description defined

    Statements

    L n = 1 π 0 π | sin ( n + 1 2 ) t | sin ( 1 2 t ) d t , subscript 𝐿 𝑛 1 𝜋 subscript superscript 𝜋 0 𝑛 1 2 𝑡 1 2 𝑡 𝑡 {\displaystyle{\displaystyle L_{n}=\frac{1}{\pi}\int^{\pi}_{0}\frac{\left|\sin% \left(n+\frac{1}{2}\right)t\right|}{\sin\left(\frac{1}{2}t\right)}\mathrm{d}t,}}
    0 references
    0 references
    n = 0 , 1 , 𝑛 0 1 {\displaystyle{\displaystyle n=0,1,\dots}}
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2addec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1addec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3addec
    0 references
    sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    C4.S14.E1.m2abdec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C1.S1.XMD7.m1gdec
    0 references