DLMF:3.11.E10 (Q1451): Difference between revisions

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Property / Symbols defined
 
Property / Symbols defined: coefficients (locally) / rank
 
Normal rank
Property / constraint
 

n = 0 , 1 , 2 , 𝑛 0 1 2 {\displaystyle{\displaystyle n=0,1,2,\dots}}

n=0,1,2,\dots
Property / constraint: n = 0 , 1 , 2 , 𝑛 0 1 2 {\displaystyle{\displaystyle n=0,1,2,\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.m2aadec
Property / Symbols used
 
Property / Symbols used: cosine function / rank
 
Normal rank
Property / Symbols used: cosine function / qualifier
 
test:

cos z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}

\cos@@{\NVar{z}}
Property / Symbols used: cosine function / qualifier
 
xml-id: C4.S14.E2.m2aadec
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.m1aadec
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.m3aadec

Latest revision as of 16:58, 1 January 2020

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DLMF:3.11.E10
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    Statements

    c n = 2 π 0 π f ( cos θ ) cos ( n θ ) d θ , subscript 𝑐 𝑛 2 superscript subscript 0 𝑓 𝜃 𝑛 𝜃 𝜃 {\displaystyle{\displaystyle c_{n}=\frac{2}{\pi}\int_{0}^{\pi}f(\cos\theta)% \cos\left(n\theta\right)\mathrm{d}\theta,}}
    0 references
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    n = 0 , 1 , 2 , 𝑛 0 1 2 {\displaystyle{\displaystyle n=0,1,2,\dots}}
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aadec
    0 references
    cos z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    C4.S14.E2.m2aadec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1aadec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3aadec
    0 references