Bessel Function of the First Kind

[Eddie W. Shore]

Blog post: http://edspi31415.blogspot.com/2016/04/h...ssell.html

HP Prime Program BESS1:

Code:

EXPORT BESS1(n,t)
BEGIN
// Bessel 1st Kind
LOCAL b;
// Integrate
b:=(1/π)*CAS.int(COS(n*X-t*SIN(X)),X,0,π);
// Approximate
b:=approx(b);
RETURN b;

END;

bess1(1,2) ≈ 0.576724807756
bess1(0,6.3) ≈ 0.223812006132
bess1(2,4) ≈ 0.364128145852