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+--- Thread: Bessel Function of the First Kind (/thread-6033.html)
Bessel Function of the First Kind - Eddie W. Shore - 04-13-2016 01:13 PM
Blog post: http://edspi31415.blogspot.com/2016/04/hp-prime-casio-classpad-bessell.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
RE: Bessel Function of the First Kind - roadrunner - 04-17-2016 04:30 PM
Nice program!
Here's a modification that's good for non integer values of order as well:
Code:
#cas
J_n(n,x):=
BEGIN
LOCAL b, t;
b:=(1/π)*int(cos(n*t-x*sin(t)),t,0,π);
IF TYPE(n)≠1 THEN
b:=b-(sin(n*π)/π)*int(e^(-x*sinh(t)-n*t),t,0,∞);
END;
RETURN approx(b);
END;
#endAnd a cool chart for n= -1, -0.5, 0, 0.5, and 1 that only took a few minutes to draw on the prime:
[attachment=3396]
-road
RE: Bessel Function of the First Kind - salvomic - 10-30-2017 09:57 PM
Thank you both of you!
There is some simple way to get also the 2nd kind Bessel function?
Salvo