Dear All,

I would like to perform a numerical integration of the following. Please let me know the method.

The integration consits of one variable essentially. Since the symbolic integration is not possibl and hence I have to do it numerically.

Appreciate you reply. Thanks

Dear Experts,

Analytical integration is not a choice for the integrals listed here. Hence, Maple is not able to find the numerical integration for the following oscillatory functions. However mathematica can. However, before I take the mathematica results, just need to check with you.

Following link shows that for a diverging series, the (Numerical) integral is finite.

http://books.google.com.sg/books?id=vntDnyh0gacC&pg=PA664&lpg=PA664&dq=nintegrate++seqlim&source=bl&ots=iNYR1o6kVd&sig=VuiQuiUMDEEGOBnguSwfcPPSHQA&hl=en&sa=X&ei=k_J4UofXJYjNkwW79IDYBw&ved=0CE4Q6AEwBA#v=onepage&q=nintegrate%20%20seqlim&f=false

1)

 Maple: 

eval(int(r^2 BesselJ(1,r)* BesselJ(0,r), r = 0..infinity)) 

Float(undefined)

Mathematica: 

NumberForm[ NIntegrate[BesselJ[0, x]*BesselJ[1, x]*x^2, {x, 0, Infinity},   AccuracyGoal -> 20], 15]

SequenceLimit::seqlim: The general form of the sequence could not be determined, and the result may be incorrect. >>

-95982.37707206068

2)  Maple:
       eval(int(r* BesselJ(0,r), r = 10..infinity)) 

                         Float(undefined)

Mathematica: 

NumberForm[ NIntegrate[BesselJ[0, x]*x, {x, 10, Infinity},   AccuracyGoal -> 20], 15]

SequenceLimit::seqlim: The general form of the sequence could not be determined, and the result may be incorrect. >>

-0.434727

Any conclusions on the result.

a) Why maple not able to evaluate the integrals.  b) Are the result of the Mathematica can be considered as appropriate.

Attached is the maple file for your consideration.

Integrations.mw 

Lookinf forward to your reply.

Thanks.

Dear Experts,

I would like to evaluate the following integral

Integrate(BesselJ(0,x)^2, x=0..Infinity).

However, it is not being evaluated in Maple.

Appreciate your response.

Dear All,

I am trying to call the maple function fsolve in the matlab. I have used maple('fsolve(x^2-4)'). It worked.

Now in the matlab code I have defined another variable. let us say a = 10.  Now I am trying to call the fsolve as follows.

maple('fsolve(a*x^2-4)')

I ended up with the following error.

Error, (in fsolve) number of equations, 1, does not match number of variables, 2

Dear All,

I would like check with you about the real form of the functions following modified bessel functions.

BesselI(0,i*x) and BesselK(0,i*x), where i is the complex variable. IS there any real form to these functions in either BesselJ and BesselY. 

I come across the BesselJ(0,i*x)  = BesselI(0,x). However, I was not able to find the converse relation.

I have not seen the complex arguments...