DLMF:25.14.E1 (Q7740)

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DLMF:25.14.E1
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    Statements

    Defining formula
    Φ ⁡ ( z , s , a ) ≡ ∑ n = 0 ∞ z n ( a + n ) s , equal-by definition Lerch-Phi 𝑧 𝑠 𝑎 superscript subscript 𝑛 0 superscript 𝑧 𝑛 superscript 𝑎 𝑛 𝑠 {\displaystyle{\displaystyle{\Phi\left(z,s,a\right)\equiv\sum_{n=0}^{\infty}% \frac{z^{n}}{(a+n)^{s}}},}}
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    DLMF id
    DLMF:25.14.E1
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    constraint
    ℜ ⁡ s > 1 , | z | = 1 formulae-sequence 𝑠 1 𝑧 1 {\displaystyle{\displaystyle\Re s>1,|z|=1}}
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