janhardo

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11 years, 39 days

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These are questions asked by janhardo

I want to have a 14 larger font instead of Times New Roman 12 for the whole worksheet or else a different font later. 
Can't make sense of how this is all organized in Maple 
You would say set a template , but ?

For Mathematica  math software app,there is a plugin to use in chatGPT pro ( paid subscription ) and maybe this can be done for Maple too ? 

Haven't used the plugin for Mathematica yet, am curious about it.
Let me have the AI look at the Riemann Hypothesis :)  
Have a few books on it, but can't get through that math with all those special functions.

How to get a general expression here ?

restart

 

f(s) is the function value  expressed as a integral around s  (singularity)  of a complex function.

f(s) = (int(f(z)/(z-s), z))/(2*Pi*I)

f(s) = -((1/2)*I)*(int(f(z)/(z-s), z))/Pi

(1)

f(s) = int(f(z)/(z - s), z)/((2*Pi)*I):

"(->)"

diff(f(s), s) = -((1/2)*I)*(int(f(z)/(z-s)^2, z))/Pi

(2)

"(->)"

diff(diff(f(s), s), s) = -((1/2)*I)*(int(2*f(z)/(z-s)^3, z))/Pi

(3)

"((ⅆ)^(n))/(ⅆn) f(s)   =  "
                                      

NULL

NULL

                 .......

quote : "Important consequence.

Above it actually says: "If there is a function f(s) that is somewhere analytic, then you can use such an integral as above to make a new function f '(s), which is also analytic there. And from that a new function f '' and so on.
That means something revolutionary for complex numbers:   "

 

================================

Question: how to get the "((ⅆ)^(n))/(ⅆn) f(s)  "?
===============================

Note : again the form of the answers in Maple : Its not possible to force Maple to come up with this form of answer, ex

``  NULL

Download Maple_primes_bvraag_hoger_orde_singulariteit_henk_hofstede.mw

Seems to me informative to see a earth-like surface on a sphere and in particular from the zeta function.
Another simple complex function will do it also.

Note: i saw a  3D picture with a colored sphere , where you can see zeroes and poles on the surface of the sphere
A colored complex function is that hard to make with Maple too?: it are all polar coordinates as complex points in the complex plane. 
The angle is standing for hue and the magnitude is standing for the lightness 

Really , the complex plotting possibilities in Maple are difficult to decipher. 

I tried something, but  in general the visualizing for me is not that easy

Now i must look at the complexplot where i got a circle for  the complexplot(sin(x + I), x = -Pi .. Pi) example ?

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