DLMF:28.5.E5 (Q8226): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12290 / rank
 
Normal rank
Property / Symbols used: Q12290 / qualifier
 
Defining formula:

S n ⁢ ( q ) subscript 𝑆 𝑛 𝑞 {\displaystyle{\displaystyle S_{n}(q)}}

S_{n}(q)
Property / Symbols used: Q12290 / qualifier
 
xml-id: C28.S5.XMD4.m1adec

Latest revision as of 14:43, 2 January 2020

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DLMF:28.5.E5
No description defined

    Statements

    Defining formula
    ( C n ⁢ ( q ) ) 2 ⁢ ∫ 0 2 ⁢ π ( f n ⁢ ( x , q ) ) 2 ⁢ d x = ( S n ⁢ ( q ) ) 2 ⁢ ∫ 0 2 ⁢ π ( g n ⁢ ( x , q ) ) 2 ⁢ d x = π . superscript subscript 𝐶 𝑛 𝑞 2 superscript subscript 0 2 𝜋 superscript subscript 𝑓 𝑛 𝑥 𝑞 2 𝑥 superscript subscript 𝑆 𝑛 𝑞 2 superscript subscript 0 2 𝜋 superscript subscript 𝑔 𝑛 𝑥 𝑞 2 𝑥 𝜋 {\displaystyle{\displaystyle(C_{n}(q))^{2}\int_{0}^{2\pi}(f_{n}(x,q))^{2}% \mathrm{d}x=(S_{n}(q))^{2}\int_{0}^{2\pi}(g_{n}(x,q))^{2}\mathrm{d}x=\pi.}}
    0 references
    DLMF id
    DLMF:28.5.E5
    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.m2abdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
    0 references
    Q12271
    Defining formula
    q = h 2 𝑞 superscript ℎ 2 {\displaystyle{\displaystyle q=h^{2}}}
    xml-id
    C28.S1.XMD10.m1ddec
    0 references
    Q12279
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C28.S1.XMD2.m1ddec
    0 references
    Q12285
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C28.S1.XMD4.m1dec
    0 references
    functions (locally)
    Defining formula
    f n ⁢ ( z , q ) subscript 𝑓 𝑛 𝑧 𝑞 {\displaystyle{\displaystyle f_{n}(z,q)}}
    xml-id
    C28.S5.XMD1.m1bdec
    0 references
    functions (locally)
    Defining formula
    g n ⁢ ( z , q ) subscript 𝑔 𝑛 𝑧 𝑞 {\displaystyle{\displaystyle g_{n}(z,q)}}
    xml-id
    C28.S5.XMD2.m1bdec
    0 references
    Q12289
    Defining formula
    C n ⁢ ( q ) subscript 𝐶 𝑛 𝑞 {\displaystyle{\displaystyle C_{n}(q)}}
    xml-id
    C28.S5.XMD3.m1adec
    0 references
    Q12290
    Defining formula
    S n ⁢ ( q ) subscript 𝑆 𝑛 𝑞 {\displaystyle{\displaystyle S_{n}(q)}}
    xml-id
    C28.S5.XMD4.m1adec
    0 references
     
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