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$s$-th derivative of $p$ at 1 equals $$\sum_{k=0}^{r}(-1)^{r-k} {r \choose k} g_s(k),$$
where $g_s$ is a polynomialspolynomial of degree $2s$. This equals 0 if $2s<r$.
$s$-th derivative of $p$ at 1 equals $$\sum_{k=0}^{r}(-1)^{r-k} {r \choose k} g_s(k),$$
where $g_s$ is a polynomials of degree $2s$. This equals 0 if $2s<r$.
$s$-th derivative of $p$ at 1 equals $$\sum_{k=0}^{r}(-1)^{r-k} {r \choose k} g_s(k),$$
where $g_s$ is a polynomial of degree $2s$. This equals 0 if $2s<r$.
$s$-th derivative of $p$ at 1 equals $$\sum_{k=0}^{r}(-1)^{r-k} {r \choose k} g_s(k),$$
where $g_s$ is a polynomials of degree $2s$. This equals 0 if $2s<r$.