EJS Special Functions Model shows how to access special functions in the OSP numerics package. The simulation displays a graph of the special function over the given range as well as the value of the selected function at a single point.

The following special functions can be displayed:

• Legendre polynomials Pn(x)
  
• associated Legendre functions Pnm(x)
  
• Laguerre polynomials Ln(x)
  
• associated Laguerre polynomials Lnm(x)
  
• Chebyshev polynomials of the first kind Tn(x)
  
• Chebyshev polynomials of the second kind Un(x)
  
• Bessel functions Jn(x)

The EJS Multiple Slit Diffraction model allows the user to simulate Fraunhofer diffraction through single or multiple slits. The user can modify the number of slits, the slit width, the slit separation and the wavelength of the incident light. The scale of the diffraction pattern can also be changed and a plot of the light intensity can be toggled on and off with a checkbox.

The Special Functions Model was created using the Easy Java Simulations (Ejs) modeling tool.  It is distributed as a ready-to-run (compiled) Java archive.  Double clicking the ejs_math_SpecialFunctions.jar file will run the program if Java is installed.  Ejs is a part of the Open Source Physics Project and is designed to make it easier to access, modify, and generate computer models.

Please note that this resource requires at least version 1.5 of Java.