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    Closed form and small-$a$ expansion of $\sum_n ne^{-an}$

    P-TRIV-RA55

    Area
    Real Analysis
    Status
    draft
    Contents

    Consider the function \(J ( a ) = \sum _ { n = 0 } ^ { \infty } n e ^ { - a n }\) defined for positive a .

    1. Write an explicit expression for J(a).

    2. Expand J(a) around the point a = 0 up to \(O ( a ^ { 0 } )\)

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