Suma de la serie (ln(x)^n)*(x-e)/(n-e)

  //        /                     pi*I\                /      -1       \\     //        /                     pi*I\                /      -1       \\
  ||lerchphi\log(x), 1, (-1 + E)*e    /*log(x)  for And\x >= e  , x < E/|     ||lerchphi\log(x), 1, (-1 + E)*e    /*log(x)  for And\x >= e  , x < E/|
  ||                                                                    |     ||                                                                    |
  ||                oo                                                  |     ||                oo                                                  |
  ||              ____                                                  |     ||              ____                                                  |
  ||              \   `                                                 |     ||              \   `                                                 |
x*|<               \       n                                            | - E*|<               \       n                                            |
  ||                \   log (x)                                         |     ||                \   log (x)                                         |
  ||                /   -------                        otherwise        |     ||                /   -------                        otherwise        |
  ||               /     n - E                                          |     ||               /     n - E                                          |
  ||              /___,                                                 |     ||              /___,                                                 |
  ||              n = 1                                                 |     ||              n = 1                                                 |
  \\                                                                    /     \\                                                                    /

$$x \left(\begin{cases} \Phi\left(\log{\left(x \right)}, 1, \left(-1 + e\right) e^{i \pi}\right) \log{\left(x \right)} & \text{for}\: x \geq e^{-1} \wedge x < e \\\sum_{n=1}^{\infty} \frac{\log{\left(x \right)}^{n}}{n - e} & \text{otherwise} \end{cases}\right) - e \left(\begin{cases} \Phi\left(\log{\left(x \right)}, 1, \left(-1 + e\right) e^{i \pi}\right) \log{\left(x \right)} & \text{for}\: x \geq e^{-1} \wedge x < e \\\sum_{n=1}^{\infty} \frac{\log{\left(x \right)}^{n}}{n - e} & \text{otherwise} \end{cases}\right)$$

x*Piecewise((lerchphi(log(x), 1, (-1 + E)*exp_polar(pi*i))*log(x), (x < E)∧(x >= exp(-1))), (Sum(log(x)^n/(n - E), (n, 1, oo)), True)) - E*Piecewise((lerchphi(log(x), 1, (-1 + E)*exp_polar(pi*i))*log(x), (x < E)∧(x >= exp(-1))), (Sum(log(x)^n/(n - E), (n, 1, oo)), True))