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DLMF:1.14.E16 - MaRDI portal

DLMF:1.14.E16 (Q477)

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DLMF:1.14.E16
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    Statements

    DLMF defining formula
    ∫ 0 ∞ ( F s ⁢ ( x ) ) 2 ⁢ d x = ∫ 0 ∞ ( f ⁢ ( t ) ) 2 ⁢ d t . subscript superscript 0 superscript subscript 𝐹 𝑠 𝑥 2 𝑥 subscript superscript 0 superscript 𝑓 𝑡 2 𝑡 {\displaystyle{\displaystyle\int^{\infty}_{0}(F_{s}(x))^{2}\mathrm{d}x=\int^{% \infty}_{0}(f(t))^{2}\mathrm{d}t.}}
    0 references
    Symbols used
    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aodec
    0 references
    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3andec
    0 references
    sine transformation of f ( t )
    DLMF defining formula
    F s ⁢ ( x ) subscript 𝐹 𝑠 𝑥 {\displaystyle{\displaystyle F_{s}(x)}}
    xml-id
    C1.S14.XMD5.m1cdec
    0 references

    Identifiers

     
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