I'm trying to find an approximation for a function that's near y = x^(1/5).
Unfortunately, polynomial approximations for functions below degree 1 don't work. These work if I specify the form manually, but are off by about 5% in the ranges I care about:
FindFit[{{1,1},{1.6875,2},{4.234567901,3},{10.71875,4},{25,5},{53.1797839,6},{104.142857,7},{190.10937,8},{327.189300,9},{535.9375,10}},{a*x^(1/5) + b*x^(1/3) + c*x + d*(1/x) + e},{a,b,c,d,e},x]
1.6616*x^(1/5) + 0.570547*x^(1/3) + -0.00136863*x + -1.445*(1/x) + 0.251113
NonlinearModelFit[{{1,1},{1.6875,2},{4.234567901,3},{10.71875,4},{25,5},{53.1797839,6},{104.142857,7},{190.10937,8},{327.189300,9},{535.9375,10}},{a*x^(1/5)+b*x^(1/3)+c*x+d*(1/x)+e},{a,b,c,d,e},x]
0.251113 - 0.00136863 x + 0.570547 x^(1/3) + 1.6616 x^(1/5) - 1.445/x
FindFit example see https://reference.wolfram.com/language/ref/FindFit.html
NonlinearModelFit example see https://reference.wolfram.com/language/ref/NonlinearModelFit.html
The problem is that I need to explore more forms or provide more data, but I'm limited to 200 characters.
How do I tell it to show the data field beneath the prompt so that I can enter the points {{1,1},{1.6875,2},..} separately? For example:
https://www.wolframalpha.com/input?i=polynomial+fit
https://www.wolframalpha.com/input?i=cubic+fit+calculator
I've tried:
FindFit[%,{a*x^(1/5) + b*x^(1/3) + c*x + d*(1/x) + e},{a,b,c,d,e},x]
find fit
<a_whole_bunch_of_other_stuff_over_a_few_days>
But they don't work and I'm tearing my hair out.. this feels like a huge oversight or even a bug. Does anyone know the magic incantation to show the data field for any query? Or to submit the data and reference it in the next query? Similar to these, but allowing me to enter the form of the equation:
