Note: the integration and approximation are two separate steps. They need to be in order for this program to work correctly.
Wednesday, April 13, 2016
HP Prime, Casio Classpad: Bessell Functions of the 1st Kind
Bessel Function of the First Kind
The program BESS1 calculates the Bessel function of the First Kind. With the HP Prime and Casio Classpad, and any calculators that can process integrals (and the processor is fast enough), we can use the definition:
J_n(x) = 1/π * ∫ (cos(n*t – x*sin(t)) dt for t= 0 to t = π
This is the solution to the differential equation:
x^2*y’’ + x*y’ + (x^2 – n^2)*y = 0, where y is a function of x.
There are many other variations and approximations to calculate J_n(x) if the integral function is not available on your calculator.
More information on the Bessel function is found here:
Casio Classpad (fx-CP400): The Function BESS1
As the screen above shows, I used a Define statement in the Main Mode:
Define bess1(n,x) = 1/π ∫ (cos(n*t – x*sin(t)) dt, from t = 0 to t = π)
Note: Make sure that the calculator is in Radians mode before calculating.
HP Prime: BESS1
// Bessel 1st Kind
bess1(1,2) ≈ 0.576724807756
bess1(0,6.3) ≈ 0.223812006132
bess1(2,4) ≈ 0.364128145852
This blog is property of Edward Shore, 2016.
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