Appell series
Okay kiddo, have you ever played with building blocks before? Appell series is kind of like building a tower out of blocks.
We start with a block at the bottom. Then we add another block on top of it, but this block is a little bit smaller than the first one. We keep adding smaller and smaller blocks on top of each other until we finish our tower.
Appell series is like that tower, but with numbers instead of blocks. Instead of starting with a big number and going smaller, we start with a small number and go bigger.
We start by picking a number, let's say 2. Then we add another number to it, let's say 4, but this time we multiply it by something before we add it. Let's say we multiply it by 3. So we have 2 + (3x4).
Now we pick another number, let's say 6, and we multiply it by something different before we add it to our first two numbers. Let's say we multiply it by 5. So we have 2 + (3x4) + (5x6).
We just keep doing this, picking new numbers and multiplying them by something different each time before we add them to our growing series. This is what makes it an Appell series!
And just like building a tower, we can keep going with this series for as long as we want.
So that's Appell series–a way of building a series of numbers by adding and multiplying different numbers together in a specific way.
We start with a block at the bottom. Then we add another block on top of it, but this block is a little bit smaller than the first one. We keep adding smaller and smaller blocks on top of each other until we finish our tower.
Appell series is like that tower, but with numbers instead of blocks. Instead of starting with a big number and going smaller, we start with a small number and go bigger.
We start by picking a number, let's say 2. Then we add another number to it, let's say 4, but this time we multiply it by something before we add it. Let's say we multiply it by 3. So we have 2 + (3x4).
Now we pick another number, let's say 6, and we multiply it by something different before we add it to our first two numbers. Let's say we multiply it by 5. So we have 2 + (3x4) + (5x6).
We just keep doing this, picking new numbers and multiplying them by something different each time before we add them to our growing series. This is what makes it an Appell series!
And just like building a tower, we can keep going with this series for as long as we want.
So that's Appell series–a way of building a series of numbers by adding and multiplying different numbers together in a specific way.