We approximate $\varphi _ { n } ( x )$ using partial sums $$S _ { m } = \sum _ { p = 0 } ^ { m } ( - 1 ) ^ { p } a _ { p } \quad \text { with } \quad m \in \mathbb { N } \quad \text { and } \quad a _ { p } = \frac { 1 } { p ! ( n + p ) ! } \left( \frac { x } { 2 } \right) ^ { n + 2 p }$$ Write a Maple or Mathematica function, CalculPhi, with arguments $(n, x, \varepsilon)$ returning an approximate value of $\varphi _ { n } ( x )$ to within $\varepsilon$. The coefficients $a _ { p }$ will be calculated by recursion.
We approximate $\varphi _ { n } ( x )$ using partial sums
$$S _ { m } = \sum _ { p = 0 } ^ { m } ( - 1 ) ^ { p } a _ { p } \quad \text { with } \quad m \in \mathbb { N } \quad \text { and } \quad a _ { p } = \frac { 1 } { p ! ( n + p ) ! } \left( \frac { x } { 2 } \right) ^ { n + 2 p }$$
Write a Maple or Mathematica function, CalculPhi, with arguments $(n, x, \varepsilon)$ returning an approximate value of $\varphi _ { n } ( x )$ to within $\varepsilon$. The coefficients $a _ { p }$ will be calculated by recursion.