What is the closed form expression for the sum: Σx2/n! from 0 to N?

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SUMMARY

The closed form expression for the finite sum Σx^n/n! from 0 to N is a polynomial, confirming that polynomials are considered closed forms by certain definitions. For the infinite case, the sum converges to an exponential function. The discussion highlights a typographical error in the original equation, clarifying that the exponent should be "n" instead of "2".

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aaaa202
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Is there a closed form expression for the sum:

Σx2/n! from 0 to N

for N=∞ it is an exponential but what about the finite case?
 
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aaaa202 said:
for N=∞ it is an exponential but what about the finite case?
Hi aaaa202:

The finite sum is a polynomial expression. According to some definitions of "close form" a polynomial is closed. I am pretty sure there is no simpler representational, as there is for the infinite sum.

BTW: You have a typo in the equation:
aaaa202 said:
Σx2/n! from 0 to N
The exponent should be "n", not "2".

Good luck.

Regards,
Buzz
 

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