Okay kiddo, let's talk about little q-jacobi polynomials.
First, let's understand what a polynomial is. You know how when you add or subtract numbers like 2+3 or 5-1, you get a new number as an answer? Well, a polynomial is like doing that same thing but with letters instead of numbers. It's an expression made up of letters and numbers that you can add, subtract, and even multiply together!
Now, little q-jacobi polynomials are a specific type of polynomial that mathematicians use to solve problems related to things like physics and statistics. They are named after a man named Carl Gustav Jacob Jacobi who was really smart and figured out a lot of cool math things.
The "little q" part of the name refers to something called a "q-number," which is sort of like a special type of number that is used in some math formulas. It's kind of like when you count by twos, you are using a special way of counting that is different from just counting by ones.
So, a little q-jacobi polynomial is a specific type of polynomial that uses these "q-numbers" in its formula. It helps solve problems related to things like energy levels in atoms or the probability of certain events happening in statistics.
Overall, little q-jacobi polynomials are basically just a type of math equation that really smart people use to solve tough problems. But don't worry, when you're a bit older you'll learn how to use them too!