# Questions tagged [difference-equations]

Difference equations, including linear and nonlinear equations, discrete version of topics in analysis, partial difference equations, oscillation theory, periodic solutions, almost periodic solutions, bifurcation theory, stability theory.

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### Double q-analog of Pochhammer

Has the function $$(z;q_1,q_2)_\infty := \prod_{n_1,n_2=0}^\infty (1-z \, q_1^{n_1} q_2^{n_2}), \quad |q_1|,|q_2|<1$$ been studied in the math literature? For example, does it obey any difference ...
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### Change of variable formulas in discrete calculus?

Crossposted from MSE. In discrete calculus one defines the $h$-difference operator $$\Delta_h[f(x)] = f(x+h) - f(x)$$ and we often define $\Delta = \Delta_1.$ We can similarly define the indefinite ...
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### Coefficient growth upper bound of a recurrence relation

Consider the recurrence relation one can obtain from the radial Schrödinger equation for the hydrogen atom, where $\psi(r)=\sum_{n=0}^{\infty} a_nr^n$: $$(n+3)(n+2)a_{n+2}+2a_{n+1}=2|E|a_n, n\geq0$$ ...
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