DLMF:2.10.E14 (Q1001)

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DLMF:2.10.E14
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    Statements

    Defining formula
    S ⁢ ( α , β , n ) = e i ⁢ β e i ⁢ β - 1 ⁢ ( e i ⁢ ( n - 1 ) ⁢ β ⁢ n α - 1 + ∑ j = 1 n - 1 e i ⁢ j ⁢ β ⁢ ( j α - ( j + 1 ) α ) ) . 𝑆 𝛼 𝛽 𝑛 superscript 𝑒 𝑖 𝛽 superscript 𝑒 𝑖 𝛽 1 superscript 𝑒 𝑖 𝑛 1 𝛽 superscript 𝑛 𝛼 1 superscript subscript 𝑗 1 𝑛 1 superscript 𝑒 𝑖 𝑗 𝛽 superscript 𝑗 𝛼 superscript 𝑗 1 𝛼 {\displaystyle{\displaystyle S(\alpha,\beta,n)=\frac{e^{i\beta}}{e^{i\beta}-1}% \left(e^{i(n-1)\beta}n^{\alpha}-1+\sum_{j=1}^{n-1}e^{ij\beta}\left(j^{\alpha}-% (j+1)^{\alpha}\right)\right).}}
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    DLMF id
    DLMF:2.10.E14
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    comment
    Warning: Falling back to standard tex;
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    Symbols used
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2acdec
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