Hi All,
With the enclosed details & notebook. I am trying to find the symbolic components of the coefficients of the FindFit function at the end. Below are the details of my workings. Here below are the basic components for symbolic representation of the coefficients of the final FindFit function.
{Sq5 = 5^2, Sq3 = 3^2};
then we take the following sequence :-
Table[ 4*i^2 - 9*i + 6, {i, 1, 10}]
= {1, 4, 15, 34, 61, 96, 139, 190, 249, 316}; then I multiply the above sequence by Sq5
Table[ (4*i^2 - 9*i + 6)*Sq5, {i, 1, 10}]
= {25, 100, 375, 850, 1525, 2400, 3475, 4750, 6225, 7900};
then I apply the following NSolve & get the desired results..below
Table[deg /. First@NSolve[Sq3 (-9 + 8 deg) == n && deg > 0, deg], {n,
Table[ (4*i^2 - 9*i + 6)*Sq5, {i, 1, 10}]}]
= {1.47222, 2.51389, 6.33333, 12.9306, 22.3056, 34.4583, 49.3889, \ 67.0972, 87.5833, 110.847}
then if I apply the FindFit function & we get the desired numerical result - which is great!
newTfKnown4 =
a x^2 + b x + c /.
FindFit[Table[
deg /. First@NSolve[Sq3 (-9 + 8 deg) == n && deg > 0, deg], {n,
Table[ (4*i^2 - 9*i + 6)*Sq5, {i, 1, 10}]}],
a x^2 + b x + c, {a, b, c}, x]
= 3.20833 - 3.125 x + 1.38889 x^2
Now - back to my original question :- From the output given above here - 3.20833 -3.125 x+1.38889 x^2 I am trying to find the symbolic representation of these 3 coefficients based off the above formulas in the NSolve above AND using the symbolic placeholders Sq3 & Sq5.
Can you recommend any approach on how to find each of the 3 coefficients so they can be represented using Sq3 & Sq5?
Many thanks for your help & attention. Best regards, Lea...
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