## 355 Reputation

8 years, 361 days

## Calculating a sum and subsequently takin...

Maple 2015

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?

## Plotting many Riemann Surfaces...

Maple 2018

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

???

## Product Expansion...

Maple 2018

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?

## Visualization of 2-dimensional map...

Maple 2018

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 ?

## numeric integration fails?...

Maple 18

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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