Bessel Function Calculator

Bessel Function in MATLAB

There are two linearly dependent solutions to the general solution of Bessel’s differential equation:

\( Y = A Jν(x)+B Yν(x) \)

1- Bessel Function of First Kind

For all real values of v, the Bessel function of the first kind, Jv(x), is finite at x=0.

• BesselJ(nu, z) = Y For each component of array Z, this returns the Bessel function of the first kind.
• If the Bessel function is to be scaled exponentially, we must use the formula Y = besselJ(nu, Z, scale). Scale values range from 0 to 1, with 0 indicating no scaling is necessary and 1 indicating that scaling is essential for the output.
• The input arguments are nu and z, where nu is the equation order. Z may be a multidimensional array, a vector, or a scalar.

2- Bessel Function of Second Kind

• Y equals besselY(nu, Z). Each element in array Z calculates the Bessel function of the second kind, Yv(x).
• If Y = besselY(nu, Z, scale), then: This indicates whether to scale the Bessel function exponentially. Scale values range from 0 to 1, with 0 showings no scaling is necessary and 1 indicating that scaling is required for the output.
• The input arguments are nu and z, where nu is the equation order. Z may be a multidimensional array, a vector, or a scalar.

3- Bessel Function of Third Kind

• besselh(nu, Z) = H. The Hankel function is calculated for each element in array Z.
• besselh(nu, K, Z) = H. With K being either 1 or 2, this calculates the first- or second-order Hankel function for each member in array Z. If K is 1, the first kind of Bessel function is computed; if K is 2, the second kind of Bessel function is calculated.
• The Bessel function can be scaled exponentially or not using the formula H = besselH(nu, K, Z, scale). If the scale value is 0, no scaling is necessary; if it is 1, we must scale the output following the value of K.

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