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Sep
20
comment Recurrence relation for a function with an integral of the function?
this looks like the right direction I think the miraculous cancellations are a feature, not a bug haha
Sep
20
comment Recurrence relation for a function with an integral of the function?
well, the more I looked at the "simplified" example I gave the more I realized that it just wouldn't do. The itnegral from 0 to 0 would be 0 and then g(1) would = 0 instead of the given starting condition of 1. The answer is most definitely not constant. I suspect it is a differential equation of the form above.
Sep
20
comment Recurrence relation for a function with an integral of the function?
where a, b and c are all functions of f
Sep
20
comment Recurrence relation for a function with an integral of the function?
A friend suggested that the correct approach is differentiating the function thrice. However, I gave that an elementary stab using the Leibniz rule definitions I found online and I couldn't get rid of the integral itself. The solution should most likely be a differential equation in the form g'''(f) = ag''(f) + bg'(f) + c*g(f), which I should hopefully then be able to solve into g(f)
Sep
20
comment Recurrence relation for a function with an integral of the function?
the fact that there is an initial condition suggested this is the approach, but I just cannot make it work
Sep
20
comment Recurrence relation for a function with an integral of the function?
that is perfect. thank you!