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Dec
15 |
awarded | Teacher |
Sep
24 |
comment |
Howto plot a specific complex function
Done, thanks. . |
Sep
24 |
awarded | Scholar |
Sep
24 |
accepted | Howto plot a specific complex function |
Sep
17 |
comment |
Howto plot a specific complex function
Thank you Loïc for the suggestion! We will make an attempt to user your proposed method. |
Sep
16 |
comment |
Howto plot a specific complex function
Thanks for your input Carlo! Solving it numerically is fully acceptable for us also, and this is what we have tried however without full success so far. I think the problem that we have not been able to circument in our naïve approach using the "fminsearch" Matlab function to numerically solve (1) is that both $\alpha(\omega)$ and $\beta(\omega)$ need to be positive. In addition, taking the power $a+1$ of the complex variable $k$ (that is $k^{a+1}$), is a multi-valued operation. Maybe you have some specific hint regarding ready-built methods to solve such constrained numerical minimalizations? |
Sep
16 |
revised |
Howto plot a specific complex function
Small cleanups |
Sep
16 |
revised |
Howto plot a specific complex function
I now just explicitly show in (1) that $k$ is a function of $\omega$, by writing $k(\omega)$. |
Sep
16 |
asked | Howto plot a specific complex function |
Feb
7 |
comment |
The real and imaginary parts of the Incomplete Gamma function for second argument being purely imaginary
Robert, your hint pointed me towards what I was looking for: the "generalized sine and cosine functions." More infor can be retreived e.g. from here: dlmf.nist.gov/8.21 |
Jan
26 |
comment |
Eigenfunction of local fractional derivative
From my point of view, your definition is strange, or at least it has a contra-intuitive feature: because $x$ and $\delta$ should have the same unit (e.g. some length unit), $\delta^\alpha$ will have the unit e.g. length$^\alpha$. Then $\tilde D^a f(a)$ will have the unit "meter$^{1-\alpha}$". But maybe this is OK? Please correct me if I'm wrong. |
Jan
26 |
awarded | Editor |
Jan
26 |
revised |
The real and imaginary parts of the Incomplete Gamma function for second argument being purely imaginary
Correcting typos |
Jan
26 |
comment |
The real and imaginary parts of the Incomplete Gamma function for second argument being purely imaginary
Thanks a lot Robert for the hint. I will explore this further after the week-end. I even suspect that the Lommel S1 function might possibly be written in terms of the Incomplete Gamma function, but this I need to look up in detail. Again thank you. |
Jan
25 |
comment |
Local fractional derivative that doesn't vanish on differentiable functions
I'm not sure, but maybe you could investigate the Yang local fractional derivative? |
Jan
25 |
answered | Are there analogous theorems and/or techniques for solving fractional differential equations involving the Riesz Derivative? |
Jan
25 |
asked | The real and imaginary parts of the Incomplete Gamma function for second argument being purely imaginary |