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Actually, there is an even stronger result, often called the interpolation theorem theorem, which follows from a well known-known theorem of Mittag-Leffler  :

Let (z_n)$(z_n)$ be a sequence of complex numbers with no accumulationlimit point. For For each n$n$, let l(n)$l(n)$ be any integer greater or equal to 1 and (a_nk)$1$ and for (0 <= k <= l(n)$0 \leq k \leq l(n)$, let ) complex$(a_{n, k})$ be complex numbers. Then Then there exists an entire function g(z)$g$ such that

g^(k)(z_n) = a_nk$$g^{(k)}(z_n) = a_{n,k}$$

for every n>=1$n \geq 1$ and every 0 <= k <= l(n)$0 \leq k \leq l(n)$.

That is, you can fix values for the derivative at the z_j's$z_j$'s.

Actually, there is an even stronger result, often called the interpolation theorem, which follows from a well known theorem of Mittag-Leffler  :

Let (z_n) be sequence of complex numbers with no accumulation point. For each n, let l(n) be any integer greater or equal to 1 and (a_nk) (0 <= k <= l(n) ) complex numbers. Then there exists an entire function g(z) such that

g^(k)(z_n) = a_nk

for every n>=1 and every 0 <= k <= l(n)

That is, you can fix values for the derivative at the z_j's.

Actually, there is an even stronger result, often called the interpolation theorem, which follows from a well-known theorem of Mittag-Leffler:

Let $(z_n)$ be a sequence of complex numbers with no limit point. For each $n$, let $l(n)$ be any integer greater or equal to $1$ and for $0 \leq k \leq l(n)$, let $(a_{n, k})$ be complex numbers. Then there exists an entire function $g$ such that

$$g^{(k)}(z_n) = a_{n,k}$$

for every $n \geq 1$ and every $0 \leq k \leq l(n)$.

That is, you can fix values for the derivative at the $z_j$'s.

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Malik Younsi
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Actually, there is an even stronger result, often called the interpolation theorem, which follows from a well known theorem of Mittag-Leffler :

Let (z_n) be sequence of complex numbers with no accumulation point. For each n, let l(n) be any integer greater or equal to 1 and (a_nk) (0 <= k <= l(n) ) complex numbers. Then there exists an entire function g(z) such that

g^(k)(z_n) = a_nk

for every n>=1 and every 0 <= k <= l(n)

That is, you can fix values for the derivative at the z_j's.