1
vote
1answer
45 views

Dirichlet kernel identity

My question is about Dirichlet kernel identity. Why does: $$\sum_{k=-n}^{n}e^{ikx}=1+ 2\sum_{k=1}^{n}\cos(kx)$$
2
votes
2answers
171 views

Does this Dirichlet series converge to zero?

Consider the periodic Dirichlet series that has this iterative definition: ...
1
vote
1answer
90 views

Summing Lerch Transcendents

The Lerch transcendent is given by $$ \Phi(z, s, \alpha) = \sum_{n=0}^\infty \frac { z^n} {(n+\alpha)^s}. $$ While computing $\sum_{m=1}^{\infty} \sum_{n=1}^{\infty} ...