発散級数

これは関数を使って普通の方法で計算できない物に値を付ける工夫でしょう。　インドのラマヌジャンが方程式を書いたそうです。
I am not certain of what precisely the point of a divergent series summation is. The terms do not converge, so these summation methods seem to arbitrarily assign a value to the summation which has no relation to the addition of terms. For example, the Cesaro summation uses the average of the members of the sequence of partial sums. Other than theoretical consistency with the convergent series, I fail to see any practical applications of this.