1. Bessel functions Jn(x), where n is a nonnegative integer (called the order of the Bessel function), are important fun

[answerhappygod]

1 Bessel Functions Jn X Where N Is A Nonnegative Integer Called The Order Of The Bessel Function Are Important Fun 1 (95.63 KiB) Viewed 76 times

1. Bessel functions Jn(x), where n is a nonnegative integer (called the order of the Bessel function), are important functions in physics that appear in diffraction theory involving circular apertures and also in potential theory and wave theory in cylindrical polar coordinates. They have an integral representation given by 1 Jn(x) == S S* cos(nt – sin t)dt (1) Write your own trapezoidal rule integrator to compute the zeroth and first order Bessel functions, and plot their behavior as a function of x for 0 < x < 10. Make sure that you use enough accuracy so that your plot looks smooth. (You might want to compare your results to Scipy's Bessel function: special.jv(n,x).)