RDP 9701: Inflation Regimes and Inflation Expectations Equation (18)

\begin{matrix} f_{π_{t + 1 + i}} (x) = {(1 - q)}^{i} f_{ε} (x - Π_{t}) \\ + q (\sum_{j = 1}^{i} {(1 - q)}^{j - 1}) \frac{(\int_{- \infty}^{\infty} \int_{- \infty}^{\infty} \int_{- \infty}^{\infty} f_{ε} (ε) f η (x - ε) f η (Π_{1}) \dots f η (Π_{N}) d μ d κ d ε)}{(\int_{- \infty}^{\infty} \int_{- \infty}^{\infty} f_{η} (Π_{1}) \dots f_{η} (Π_{N}) d μ d κ)} \\ \begin{matrix} i = 1, \dots, \infty \end{matrix} \end{matrix}