DLMF:1.8.E13 (Q267): Difference between revisions

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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.m2agdec
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
Defining formula:

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

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1agdec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3agdec
Property / Symbols used
 
Property / Symbols used: Q10757 / rank
 
Normal rank
Property / Symbols used: Q10757 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q10757 / qualifier
 
xml-id: C1.S1.XMD7.m1jdec

Latest revision as of 16:04, 1 January 2020

No description defined
Language Label Description Also known as
English
DLMF:1.8.E13
No description defined

    Statements

    Defining formula
    1 π ⁢ ∫ - π π f ⁢ ( x ) ⁢ g ⁢ ( x ) ⁢ d x = 1 2 ⁢ a 0 ⁢ a 0 ′ + ∑ n = 1 ∞ ( a n ⁢ a n ′ + b n ⁢ b n ′ ) , 1 𝜋 subscript superscript 𝜋 𝜋 𝑓 𝑥 𝑔 𝑥 𝑥 1 2 subscript 𝑎 0 subscript superscript 𝑎 ′ 0 subscript superscript 𝑛 1 subscript 𝑎 𝑛 subscript superscript 𝑎 ′ 𝑛 subscript 𝑏 𝑛 subscript superscript 𝑏 ′ 𝑛 {\displaystyle{\displaystyle\frac{1}{\pi}\int^{\pi}_{-\pi}f(x)g(x)\mathrm{d}x=% \tfrac{1}{2}a_{0}a^{\prime}_{0}+\sum^{\infty}_{n=1}(a_{n}a^{\prime}_{n}+b_{n}b% ^{\prime}_{n}),}}
    0 references
    DLMF id
    DLMF:1.8.E13
    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.m2agdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1agdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3agdec
    0 references
    Q10757
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C1.S1.XMD7.m1jdec
    0 references
     
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