8 years, 46 days

## How to get a general expression for de...

Maple

How to get a general expression here ?

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

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

 (2)

 (3)

.......

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:   "

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

## How to make a projection of a complex fu...

Maple

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

## How to plot a 3d Zeta function...

Maple

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 ?

## How to create a plot for the critical li...

Try to calculate the values for the Zeta(z) on the critical line in symbolic form and also as a plot

Both i did not yet succeed in

f:=z->Zeta(z);

complexplot3d(f,-1-1*I..1+1*I);

solve(f = 1/2 , z )

## How to get written out some terms of a s...

Maple

Alternating serie

 (1)

 > sum((-1)^(n + 1)/(2*n - 1), n = 1 .. infinity):

 (2)
 > expand(sum((-1)^(n + 1)/(2*n - 1), n = 1 .. 4),symbolic);
 (3)
 > ?expand
 > series(sum((-1)^(n + 1)/(2*n - 1), n = 1 .. infinity),n=0,5);
 (4)
 >
 Info series

How to get for n= 4