DLMF:6.12.E5 (Q2293)

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DLMF:6.12.E5
No description defined

    Statements

    Defining formula
    f ⁡ ( z ) = 1 z ⁢ ∑ m = 0 n - 1 ( - 1 ) m ⁢ ( 2 ⁢ m ) ! z 2 ⁢ m + R n ( f ) ⁢ ( z ) , sine-cosine-integral-f 𝑧 1 𝑧 superscript subscript 𝑚 0 𝑛 1 superscript 1 𝑚 2 𝑚 superscript 𝑧 2 𝑚 superscript subscript 𝑅 𝑛 sine-cosine-integral-f 𝑧 {\displaystyle{\displaystyle\mathrm{f}\left(z\right)=\frac{1}{z}\sum_{m=0}^{n-% 1}(-1)^{m}\frac{(2m)!}{z^{2m}}+R_{n}^{(\mathrm{f})}(z),}}
    0 references
    DLMF id
    DLMF:6.12.E5
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    Symbols used
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5addec
    0 references
    auxiliary function for sine and cosine integrals
    Defining formula
    f ⁡ ( z ) sine-cosine-integral-f 𝑧 {\displaystyle{\displaystyle\mathrm{f}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E17.m2aadec
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    Q11305
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C6.S1.XMD2.m1cdec
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    Q11308
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C6.S1.XMD3.m1dec
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    remainder term (locally)
    Defining formula
    R n ( f ) ⁢ ( z ) superscript subscript 𝑅 𝑛 sine-cosine-integral-f 𝑧 {\displaystyle{\displaystyle R_{n}^{(\mathrm{f})}(z)}}
    xml-id
    C6.S12.XMD1.m1dec
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