markweitzman

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15 years, 275 days

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These are questions asked by markweitzman

So Maple 2019 seems to be unable to evaluate a relatively easy integeral for a positive integer, but when the obvious substitution u=cos(x) is made it is able to evaluate the integral.  Is there some setting I am using that is causing Maple to give up without much effort?  
 

restart

assume(n::integer, n > 0)

about(n)

Originally n, renamed n~:
  is assumed to be: AndProp(integer,RealRange(1,infinity))

 

int(sin(x)^(2*n+1), x = 0 .. Pi)

int(sin(x)^(2*n+1), x = 0 .. Pi)

(1)

for j to 5 do int(sin(x)^(2*j+1), x = 0 .. Pi) end do

4/3

 

16/15

 

32/35

 

256/315

 

512/693

(2)

int((-u^2+1)^n, u = -1 .. 1)

GAMMA(n+1)*Pi^(1/2)/GAMMA(n+3/2)

(3)

for j to 5 do int((-u^2+1)^j, u = -1 .. 1) end do

4/3

 

16/15

 

32/35

 

256/315

 

512/693

(4)

``


 

Download walter.mw

Can anyone look at this worksheet, and explain why maple seems to complicate an easily evaluated integral?

 

 

 

Hyper.mw

 


 

 

Integrating a positive definite function (normal distribution) and a >= 0 function (Heaviside) should not return a negative value.

 

 

with(Statistics);
X := RandomVariable(Normal(1, sqrt(2.25)));
int(PDF(X, x)*Heaviside(x^7-5*x^4-3*x+1), x = -infinity .. infinity);
                         -0.08507120131

 

 

Bug.mw

Is there a way to take the laplacian of 1/r and get the "physics" answer of -4*pi*delta(\vec{r})?

My Maple worksheet is attached below - where I am solving two quantum mechanics problems, trying to find the eigenvalues for certain potentials.  Using a previous post in Mapleprime (https://www.mapleprimes.com/questions/221629-Can-Maple-Find-Solution-To-Eigenvalue),  I saw how to get the lowest eigenvalue.  My question is how using numeric solutions, I can get the higher eigenvalues and corresponding solutions.  Is there a way to specify that e (the eigenvalue) has to be in a certain range.  I tried to specify assumptions (e>0.6), but that didn't work.  I know that for the second problem (using the shooting method) that the 4 lowest eigenvalues are 0.184358, 0.70747, 1.2065, 1.5625.  Thank you very much for you consideration.

 

ODE_BVP_eigenvalues.mw

 

 

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