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
// Integrate
// Approximate


Note: the integration and approximation are two separate steps.  They need to be in order for this program to work correctly.


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

This blog is property of Edward Shore, 2016.


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

    1. Antonio,

      I 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,


    2. That gives me the error "Invalid argument".
      Sorry for annoyances.

    3. Antonio,

      What 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).

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

      Sorry for all the troubles,


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

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  3. A very interesting article. The insights are really helpful and informative. Thanks for posting.
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  4. Really its very useful information that you have shared and thanks for sharing the information with us.
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