1
vote
1answer
116 views

Limits of complex error and gamma functions in the complex plane?

What are the following one-sided limits in the complex plane (in the form $x+iy$): For the complex error function: $\lim_{x \to 0^+, y \to 0^+}\text{erf}\left(x+iy\right) = $ $\lim_{x \to +\infty, ...
7
votes
3answers
372 views

Evaluation of $\sum_{n=1}^\infty \frac{1}{\Gamma (n+s)}$

I want to try and evaluate this interesting sum: $$\sum_{n=1}^\infty \frac{1}{\Gamma (n+s)}$$ where $0 \le s < 1$ WolframAlpha evaluates this sum to be $$\sum_{n=1}^\infty \frac{1}{\Gamma ...