Okay, imagine you have a toy called a spin top. You can spin it around very fast and it makes a humming sound. Now imagine that instead of a toy, you have a special type of math equation. This equation also has a humming sound, but instead of spinning around, it's made up of special numbers called q-numbers.
The Hahn-Exton q-Bessel function is a fancy name for this equation that uses q-numbers to make a humming sound. It's kind of like a song that is made up of numbers instead of words. But this song is really important because it helps scientists understand things like vibrations and waves.
Basically, the Hahn-Exton q-Bessel function is a way to use math to describe the way things vibrate and move. It might seem complicated, but just like spinning a top, it can be really fun to learn about!