All Questions

For years umbral calculus have fascinated me. Bernoulli numbers (which represent powers of Bernoulli umbra) are involved in many classic power series expansions. Yet, it still remains mistery what ...

If we take the MacLaurin series for $\ln(x+1)$ and evaluate it at $x=-1$, we will get the Harmonic series with the opposite sign: $-\sum_{k=1}^\infty \frac1x$. Since the regularized sum of the ...