This paper is inspired by this post. It asked how to count the number of solutions of the equation with non-negative integral solution:

x_1 + ... + x_k = n

without using the standard method of line and dot counting. I transform the problem into a partial difference equation, ...

I tried to find the n-th derivative of the function sec x + tan x in a specific form, and a partial difference equation arises from it. An attemp to solve the equation is stated in another article: Reducing a partial difference equation into a partial differential equation and solving for the generating function using method of characteristics

I am going to solve a partial difference equation, firstly to transform it into a partial differential equation by using generating function method. Then, the partial differential equation can be solved by using method of characteristics.

In this how-to, I am going to solve a recurrence differential equation using Binomial Expansion Theorem for non-commutative elements.

I am going to solve a partial difference equation in this paper, which arises from binomial expansion of non-commutative matrix/operator.

This question is a forward of this post.

What is the recurrence relation of this sequence? And it's solution?

In many cases, the recurrence equations that people are solving involves index of only non-negative values. Here I have a recurrence equation which arises from transport of light in an infinite 1D chain:

where is the Kronecker delta function. i.e.:

...