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Are there a set of theorems dealing with "amount of divergence" series? Let me explain by example. The Dirchlet $\eta$ series $\sum_n (-1)^{n-1} n^{-x}$ converges when $x > 0$. We may say ...

I am trying to prove or disprove $$\sum_{k=1}^{\infty}e^{-\lambda_{k}t}c_{k} \xrightarrow{t\to 0} \sum_{k=1}^{\infty}c_{k} ,$$ where $\sum c_{k}<\infty, \sum c_{k}^{2}<\infty\text{ and }\frac{\...

Originally asked on MSE here: https://math.stackexchange.com/q/1780149/52694 Analytic functions can be decomposed into a Taylor series, and furthermore the Taylor series converges back to the ...

One could assign a value to divergent series by means of several summation methods. One summation method we could consider is the generating function method. Let's sum, for example, the fibonacci ...