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A Periodic Functional Equation

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Jul 11, 2025
13:27

We find the period of the function f(x), given the functional equation f(x) = sqrt{2 - sqrt{3}}(f(x + 1) + f(x - 1)) for all real x. Solving as a recurrence relation: https://en.wikipedia.org/wiki/Linear_recurrence_with_constant_coefficients#Order_2 00:00 Periodic functions 00:50 Substitution & elimination 04:30 f(x ± 2) 08:32 Finding the period 10:18 Smaller periods?

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A Periodic Functional Equation | NatokHD