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[MA375] Final Exam Formulas need to memorize
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EGF encoding for the sequence 1/n! from n=0 to infinity
The {1/0!, 1/1!,...} EGF is: sum from n=0 to infinity of n!*(x^n/n!) = sum from n=0 to infinity of (x^n) = 1/1-x.
Addition of 2 generating functions formula
Closed form formula for GF 1 + Closed form formula for GF 2
EGF encoding for the sequence 1+1/n! from n=0 to infinity (example of how to do transformations easily like in 9.4 "The Summation Operator" lesson)
Since regular {1,1,1,...} EGF is sum from n=0 to infinity of n!*(x^n/n!) = e^x,
The {1/0!, 1/1!,...} EGF is: sum from n=0 to infinity of n!*(x^n/n!) = sum from n=0 to infinity of (x^n) = 1/1-x.
So now we can just use the ADDITION rule for generating functions here to get:
{1,1,1,...}+{1/0!,1/1!,...} => EGF = e^x + (1/1-x)
At least k properties formula
L_k =
Exactly k properties formula
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