4 ms·
Is the author's definition consistent with that?
by mdevere 11y ago
Is the author's definition consistent with that?
- magicalist 11y agoAt first look it appears to be yes, but (and maybe the GP can explain more) I don't see how it really gives any insight into the fractional derivative. It's just subbing out the derivative operator for finite differences, and you'd still need to introduce the gamma function, so you aren't gaining much that way either. What am I missing here?
- yablak 11y agoFrom the functional form of the author's definition, it looks like yes. However, to connect the two definitions probably requires using Cauchy's integral formula (http://en.wikipedia.org/wiki/Cauchy%27s_integral_formula http://en.wikipedia.org/wiki/Cauchy%27s_integral_formula) and/or the complex method of residues, along with some line integral tricks (http://en.wikipedia.org/wiki/Methods_of_contour_integration http://en.wikipedia.org/wiki/Methods_of_contour_integration).
- yablak 11y agoBTW, I believe the "generalization" of the taylor expansion mentioned here is the Laurent series (http://en.wikipedia.org/wiki/Laurent_series http://en.wikipedia.org/wiki/Laurent_series).