For a natural number x and a polynomial function 
, we define a recursive function 
, as follows:
, we define a recursive function , as follows:
, and
, for 
.For example, if 
(or in Matlab array form, P = [1 2 1]):
(or in Matlab array form, P = [1 2 1]):
...
and so on...
We can see that can grow very quickly. Therefore, we will instead calculate: 
, that is, 
is equal to the logarithm (base-e) of the absolute value of .
can grow very quickly. Therefore, we will instead calculate: , that is, is equal to the logarithm (base-e) of the absolute value of .Given a polynomial array P, and an integer x, find the value of , rounded-off to 4 decimal places.
, rounded-off to 4 decimal places.----------------------
NOTE: To encourage vectorization , FOR and WHILE loops are disabled. If you know the math, this problem can be solved in less than 15 lines of code. However, solutions up to 50 lines of code will still be accepted. The semicolon (;), shall be considered as an end-of-line character.
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Update:
1. Up to 50 lines of code is acceptable solution.
2. Link to a website explaining recursive closed form is added.