1
vote
0answers
32 views

Convergence of a limit

everyone. I have a question regarding the convergence of a certain limit. I've been fiddling with it but its been proving quite evasive. What I am trying to calculate is the Grundwald-Letnikov ...
1
vote
0answers
69 views

How can we interpret the coefficients of Laurent series?

The coefficients of a Taylor series of a function about a given point are related to the nth derivatives of the function at that point. Can we make a similar statement about what the (negative-index) ...
3
votes
0answers
106 views

Fractal derivative of complex order and beyond

Is there some precise definition of "complex (fractal) order derivative" for all complex number? I am aware of the Riemann-Liouville fractional definition given here: Complex derivative but I would ...
1
vote
1answer
118 views

Existence of Riemann-Liouville Integral

The Riemann Liouville integral is defined as: $\frac{1}{\Gamma\left(\nu\right)}\int\limits _{h}^{t}\left(t-\xi\right)^{\nu-1}f\left(\xi\right)d\xi$ It is supposed it does exist for all $\nu>0$ and ...
7
votes
2answers
587 views

Fractional calculus in complex analysis

According to Fractional calculus, we know that $$(J^\alpha f) ( x ) = { 1 \over \Gamma ( \alpha ) } \int_0^x (x-t)^{\alpha-1} f(t) \; dt$$ It's in real analysis, but what about in complex analysis? ...