**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:

Wolfram

Wikipedia

**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**

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;

**Examples**

bess1(1,2) ≈ 0.576724807756

bess1(0,6.3) ≈ 0.223812006132

bess1(2,4) ≈ 0.364128145852

This blog is property of Edward Shore, 2016.

i dont know how install this program in my hp prime. can you help me please?¨

ReplyDeleteThank u.

Antonio,

DeleteI don't have the file for download. However, if you don't want to type in the program yourself:

1. Open the HP Prime Connectivity Kit and plug in your HP Prime. The Kit (should) recognize the Prime.

2. Copy the text that is presented in the HP Prime: BESS1 section. For convenience, the program text is in Courier font.

3. On the Connectivity Kit, click on your calculator. Expand the folders on the Calculator. If you are using Windows, right click on Programs and select New. You'll be prompted for a name. In this case, type BESS1.

4. The program editing page will open. You then can replace the pre-written text by pasting the program on the editor. Don't forget to save!

5. Optional: once the program the saved, it will be listed under the calculator on the top-left side of the Connectivity Kit screen. You can drag the program down to the lower-left side of the screen (under the bar where it says "Name" and "Size") and it will save the program as an hppprgm file on your computer.

Hope this helps,

Eddie

That gives me the error "Invalid argument".

DeleteSorry for annoyances.

Antonio

Antonio,

DeleteWhat firmware version do you have on your calculator? I find that the easiest way to find out is to press the [ Help ] key, then the (Tree) soft key, from Home Screen, scroll up and select About HP Prime.

HP Prime just updated to firmware 10077 (4/2016). ftp://ftp.hp.com/pub/calculators/Prime/

If you are still having trouble transferring the program, then you might have to type in the program yourself.

Sorry for all the troubles,

Eddie

Thank you. I just wanted to know where to ship it since I know now to keep producing it

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