Axel Vogt

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19 years, 147 days
Munich, Bavaria, Germany

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These are replies submitted by Axel Vogt

Besides Wikipedia (may differ on selected language) there are proofs and overviews at https://www.math.cmu.edu/~bwsulliv/basel-problem.pdf or https://arxiv.org/abs/2010.03953 (Apostol's double integral is quite puzzling)

@Thomas Richard 

Essentially you reduced it to Int( sin(alpha)*alpha^(r), alpha).

One step more would use Int( exp(a)*a^(r), a) and Maple solves it in terms of the Gamma function which seems more simple.

If you input integers then Maple should process on that input. Otherwise just use floats.

@Christopher2222 for sites with persistent troubles you may use https://en.wikipedia.org/wiki/Ungoogled-chromium

there are portable versions as well

Works for me too (Firefox and blocking advertising). Disabling "infinite scroll" however gives the first page only. Hm, a matter of taste I suppose

I marked it with the mouse and changed it through the menu bar (without further testing)

@sursumCorda 

Are you sure about RefineRoot? The help gives me the impression that it is for finding approximative roots.

Edit: I see, it brackets a root

@mmcdara how about this:


 

# https://www.mapleprimes.com/questions/237846-How-Can-I-Go-From-The-Lhs-To-The-Rhs

The first one is piecewise(u <= v, u, v < u, v);

piecewise(u <= v, u, v < u, v)

(1)

It means to pick the smaller one of u and v, so it is min(u,v)

min(u, v)

(2)

The second one is puzzling [piecewise(u <= 1 - v, 0, 1 - v < u, u + v - 1)];

[piecewise(u <= 1-v, 0, 1-v < u, u+v-1)]

(3)

Make the Ansatz u+v-1 = a and simplify  
``=eval(%, u = a-v+1); # u+v-1 = a
simplify(%);

"=[{[[0,a-v<=-v],[a,-v<a-v]]]"

 

`` = [piecewise(a <= 0, 0, 0 < a, a)]

(4)

which obviously is max(0,a)

max(0, a)

(5)
 

 


 

Download MP_237846_min_max_piecewise.mw

@vv Thanks - that solves it

I was trapped by numerics it seems

[seq(10.0^(20*n), n=2 .. 14)]:
[seq(expr, x in %)]:
evalf[1000](%): evalf[3](%);
[        64          104          144         183         223  
[-3.22 10  , -1.79 10   , -2.18 10   , 9.38 10   , 3.02 10   ,

          263         303         343         383         423  
  -1.08 10   , 3.41 10   , 1.07 10   , 2.35 10   , 3.16 10   ,

          462          503          543]
  -3.26 10   , -1.96 10   , -3.39 10   ]

 

 

@Rouben Rostamian  

It's not a bug, just the rationalized form of yours. And you will need to sum up to ~ 10^11 I think

p:=c*(a+b); dismantle(p);

or

ToInert(p); FromInert(%);

@mcouture Adblockers and Anti-Tracking are natural for educated web users expecting privacy. And there is a lot of snooping on https://www.maplesoft.com/Applications/ However the site can be used if anti tracking is configured with care (and time for that).

@Kitonum acer's approach works in 2017.3

x^x=1/sqrt(2); map(ln, %); solve(%);

 

Why do you think the double integral equals Pi?

And: how do you want Dirac( g(x) ) to be understood?

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