radaar

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7 years, 85 days

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These are replies submitted by radaar

@vv 

I think you are not getting my point. There is no issue with this expression. The only issue I found is when using the series expansion for hyper geometric function I.e. hypergeom([3/2-n-2 I,1/2],[3/2],...)

@vv 

So using the first equation is fine right? rather than going for analytical equation.

@vv 

The summation index i and q has upperlimt as infinity. See the series expansion of hypergeometric function and some further changes leads to this triple sum equation with appel hypergeometric function. Both are same. My question is why series expansion causes convergence issues. When the upper index of i is more than q it diverges. The first one is not closed form equation. The second one is a closed form equation. Still there is convergence issue.

problem3.mw

@vv 

See the following code which I have already posted. Does it converges or not. The expression in the below file is same as above. For that question I got answer that it will not converge. Here for the same the answer is converging.

PROBLEM.mw

@Mariusz Iwaniuk 

The new question which i posted is the same. But this is the corresponding analytical equation for that. There you told that it converges on increasing q. Here you are telling the opposite. As I told in the other one series expansion of  the hypergeometric function  gives the above equation. So my question is why it is not converging when we do the hypergeometric series ex[pansion. see the code below.

PROBLEM1.mw

@Mariusz Iwaniuk 

I am asking when you expand the hypergeometric function.

@Mariusz Iwaniuk 

  The reason for series expansion is atlast i will get an analytical solution. But series expansion with your code returns the input.

No_problem_1.mw

@Mariusz Iwaniuk 

   Then increase i again it diverges. both sums upper index is infinity.

 

problem3.mw

@Markiyan Hirnyk 

Can it be a bug in the software

@Markiyan Hirnyk 

   I have already stated that I have two equations 1) integral equation 2) the corresponding analytical equation. The integral equation gives me converged result where as analytical (posted) equation shows divergence. There is no typo too.

@Carl Love 

   The integral equation for the same is converging. So this must converge.

@Kitonum 

  I tried approximate int option and got the following result

integral7.mw

@Kitonum 

The last step is not evaluated even with numerical integration in the following code


 

restart; a := 2; Q := 5.48; d := 6.48; chi := (1/4)*Pi; phi := 0.; p := 5/2; x := freeze((a*sin(CHI)*sin(phi)+d*cos(chi))^2+(a*cos(CHI)+d*sin(chi))^2); y := freeze(2*Q*((a*sin(CHI)*sin(phi)+d*cos(chi))^2+(a*cos(CHI)+d*sin(chi))^2)^(1/2)); int(1/(Q^2+x+y*cos(beta))^p, beta)

qq := int(1/(Q^2+x+y*cos(beta))^p, beta = 0 .. 2*Pi):

qqq := evalf(Int(zz, CHI = 0 .. Pi))

Warning,  computation interrupted

 

NULL

NULL


 

Download INTEGRAL_NEW3.mw

@vv how to check integral exist or not

@Mariusz Iwaniuk 

But i am running a loop over epsilon and this sum is not converged at m=35. I need much more fast.

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