MATLAB: How to symbolically solve this Bessel function

besselsymbolic

I need to solve the following bessel function:

J1(z)=(1/(2*pi*i))*int(exp(i*z*cos(θ))*cos(θ)),θ,0,2*pi),

where z=a*(x+k), a:real, 0<=k,=1.

Could anyone please guide me? It is the first time I deal with a problem like this and I cannot completely figure out what I should do. I need the solution to be a function of x.

Best Answer

The best you can likely do is the core MATLAB besselj function.

If you have the Symbolic Math Toolbox, use its besselj function.

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MATLAB: Bessel functions

I have solved this issue. I should have started the iterations at 0 instead of 1.

Thread closed. Thanks

MATLAB: Does Maple return terms with a function “erfi” that cannot be understood by Symbolic Math Toolbox or MATLAB

The term erfi(x) is Maple's representation of the imaginary error function. There is no exact equivalent symbolic function in Symbolic Math Toolbox (the closest is the MATLAB function ERF in MATLAB).

To work with such expressions, convert the term erfi into terms that MATLAB can understand. From the Maple help this function is defined as,

 erfi(x) = 2/sqrt(pi) * int(exp(t^2), t=0..x)

You can use the following expression to convert this into a MATLAB symbolic expression

syms x t
myErfi=2/sqrt(pi) * int(exp(t^2),0,x)

Additional help for Maple can be found by typing

mhelp erfi

Note that Symbolic Math Toolbox uses MuPAD as its symbolic engine as of Symbolic Math Toolbox 5.1 (R2008b). Therefore, the MHELP function will not work if MuPAD is the active symbolic engine.

Best Answer

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MATLAB: Does Maple return terms with a function “erfi” that cannot be understood by Symbolic Math Toolbox or MATLAB

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