Plotting an equation with summation and roots of bessel function

where y=M(t)/M(infinity), alpha(n) are roots of bessel function (first kind, zero order)

D and a are constants, D=5.46e-4, a=3

I'm trying to plot (t,y) for t=0:1:300 but not sure how to code for the roots of bessel function part. Any help is greatly appreciated, thank you!

[darova]

Here is the bessel. What is the value of ν?

[J. Alex Lee]

check this: https://www.mathworks.com/matlabcentral/answers/230834-zeros-of-bessel-functions

Answer 1

[Devineni Aslesha]

The roots of the bessel function (first kind, zero order) can be obtained from the below code.

Z = 0:0.1:20;
J0 = besselj(0,Z);
alpha = roots(J0);

For more information, refer the following links.

https://www.mathworks.com/help/matlab/ref/besselj.html#bvgg_s3

https://www.mathworks.com/help/matlab/ref/roots.html

[J. Alex Lee]

this does not seem right...

[Devineni Aslesha]

I apologize for the above answer. However, the roots of the bessel function can be found using roots function from the given File Exchange link.