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DLMF:6.12.E6 - MaRDI portal

DLMF:6.12.E6 (Q2992)

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DLMF:6.12.E6
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    Statements

    DLMF defining formula
    g ⁡ ( z ) = 1 z 2 ⁢ ∑ m = 0 n - 1 ( - 1 ) m ⁢ ( 2 ⁢ m + 1 ) ! z 2 ⁢ m + R n ( g ) ⁢ ( z ) , sine-cosine-integral-g 𝑧 1 superscript 𝑧 2 superscript subscript 𝑚 0 𝑛 1 superscript 1 𝑚 2 𝑚 1 superscript 𝑧 2 𝑚 superscript subscript 𝑅 𝑛 sine-cosine-integral-g 𝑧 {\displaystyle{\displaystyle\mathrm{g}\left(z\right)=\frac{1}{z^{2}}\sum_{m=0}% ^{n-1}(-1)^{m}\frac{(2m+1)!}{z^{2m}}+R_{n}^{(\mathrm{g})}(z),}}
    0 references
    Symbols used
    Q10729
    DLMF defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aedec
    0 references
    auxiliary function for sine and cosine integrals
    DLMF defining formula
    g ⁡ ( z ) sine-cosine-integral-g 𝑧 {\displaystyle{\displaystyle\mathrm{g}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E18.m2aadec
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    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C6.S1.XMD2.m1ddec
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    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C6.S1.XMD3.m1adec
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    remainder term (locally)
    DLMF defining formula
    R n ( g ) ⁢ ( z ) superscript subscript 𝑅 𝑛 sine-cosine-integral-g 𝑧 {\displaystyle{\displaystyle R_{n}^{(\mathrm{g})}(z)}}
    xml-id
    C6.S12.XMD2.m1dec
    0 references

    Identifiers

     
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