digerdiga

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These are questions asked by digerdiga

I have this sum which should be equal to argument(GAMMA(I*x)) with x>0.

restart;

`assuming`([x*ln(n)-(1/2)*Pi-(sum(arctan(x/k), k = 1 .. n))], [x > 1]);

aG := `assuming`([limit(%, n = infinity)], [x > 1]);

`~`[evalf](eval([aG, argument(GAMMA(I*x))], x = 1))

 

However this limit evaluation is somehow broken in as it always gives some order symbol O(1) etc..

What is happening here?

Hello,

When 3d-Plotting a function say f(z)=sqrt(z)=sqrt(x+I*y) then Maple automatically only plots the principal branch.

In the example above is it possible to plot the second surface too?

Is it also possible to plot the full continuous Riemann surface as in

https://en.wikipedia.org/wiki/Riemann_surface#/media/File:Riemann_sqrt.svg

or

http://mathworld.wolfram.com/RiemannSurface.html

 

???

The following product gives 0

restart;

product(1-1/k, k = 2 .. infinity);


                               0

However when I expand the product

1 - 1/2 - 1/3 - 1/4 - ... + 1/2*1/3 + 1/2*1/4 + ... + 1/3*1/4 + ... + triple products + quadruple products + and so forth...

Now the double, triple, quadruple, and so forth sums of products converge.

The 1/2 + 1/3 + 1/4 + ... nevertheless diverges, so why does maple give me 0?

Suppose I have a subset of R^2, say (x,y) € [0,1] x [0,1]

Now I map

x=r*exp(t)

y=r*exp(-t)

Is it possible to do a 2d contourplot to just see where [0,1]x[0,1] is mapped onto ?

I tried to integrate

int((1-x^floor(u))/((1-x)*u^2), u = 1 .. infinity, numeric)

where x=-1. The result should be log 2 = 0.6931471806. However it gives me 0.6687714032.

When using a numeric cut off, the result improves, so what is the issue here?

6687714032

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