EDB — 1BP

Exercises

1. [1BP] Prerequisites:[1G2]↺↻.Let \(a∈ℝ\), let \(I\) be open interval with \(a∈ I\), and \(𝜑_ 0:I→ℝ\) continuous.

   We recursively define \(𝜑_ n:I→ℝ\) for \(n≥ 1\) via \(𝜑_{n}(x)=∫_ a^ x 𝜑_{n-1}(t)\, {\mathbb {d}}t\); show that

   \begin{equation} 𝜑_{n+1}(x)=\frac 1{n!} ∫_ a^ x (x-t)^ n𝜑_ 0(t)\, {\mathbb {d}}t \label{eq:multi_ primitiva} \end{equation}

   1

   Solution 1

   [1BQ]↺↻