Puzzle time - Recovering the Polynomial

[Klaus]

The Oracle at Delphi has in mind a certain polynomial p (in the variable x, say) of degree d with arbitrary real-valued coefficients. You may query the Oracle with any integer n>=0, and the Oracle will tell you the value of the n-th derivative of p at x = 3.1415927.

How many queries do you have to make to determine p?

Hint: Jolly already almost gave away the solution today.

[Horace]

Right taylor series exactly QED.

[Klaus]

@Horace said in Puzzle time - Recovering the Polynomial:

Right taylor series exactly QED.

Somebody was awake in Calculus 101!