MATLAB CODE of an equation including Bessel's function

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Md Jahid Hasan Sagor 2022-8-17

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https://ww2.mathworks.cn/matlabcentral/answers/1781090-matlab-code-of-an-equation-including-bessel-s-function

编辑： Torsten 2022-8-18

I am stuck coding the below equation. Would you please give me some guidance? I know f and beta. I need to know gamma(f,beta). Here, alpha are the zeros of the bessel function J1(x). How can I approximate the solution as it goes to infinity.

Please, would anyone kindly help me, how can I approach it?

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Answer 1

Torsten 2022-8-17

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https://ww2.mathworks.cn/matlabcentral/answers/1781090-matlab-code-of-an-equation-including-bessel-s-function#answer_1028345

编辑：Torsten 2022-8-17

Here is a very similar problem solved:

https://de.mathworks.com/matlabcentral/answers/1777535-infinite-sum-with-bessel-s-function?s_tid=srchtitle

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Torsten 2022-8-18

编辑：Torsten 2022-8-18

在 MATLAB Online 中打开

In my case, alpha_k are the zeros of J1(x). I understand that I need to use your function J0ROOTS to find out zeros of J1(x). My question is, will the no. Zeros be equal to the no. of Summation? For example: if I find out first 10 zeros, should I sum up k=1 to 10?

You have an infinite sum. The terms of this sum can be evaluated up to the value of k for which you have alpha_k, the k-th zero of J1(x). So you can only sum up to the k which you choose for the number of zeros supplied for J1.

You used sum(function,2) in the for loop. Does it help me to calculate K=1 to inf?

In the code, the sum over the columns of the matrix

2*besselj(0,a_k.*r)./(a_k.^2.*besselj(1,a_k)).*exp(-a_k.*t(i))

gives L(r,t(i)) , summed up from k=1 to k = n, not k = Inf, as a column vector with r = (0:0.01:1).'

Choose n big enough such that the difference between the finite and infinite sum becomes small enough for your purpose. Practically, test what comes out if you vary n.

Md Jahid Hasan Sagor 2022-8-18