Hi, i have a question about a proof of some recursive equation,(adsbygoogle = window.adsbygoogle || []).push({});

the function is

$$c_{n}(a)=\int_{0}^{\pi } \frac{cos(nx)-cos(na)}{cos(x)-cos(a)}$$

whit ##n\in \mathbb{N}## and ##a\in \mathbb{R}## .

whit some algebra is easy to see ##c_{0}(a)=0## and ##c_{1}(a)=\pi##

and the recursive equation

$$c_{n+1}(a)+c_{n-1}(a) -2 \, cos(a) \, c_{n}(a) =0$$

Then the author says that this is a differential equation and solves it (making ##c_{k}(a)=Ce^{sk}##)

I dont understand , i mean this is a recursive relation not a differencial equation.

so every recursive relation can be solve with a differencial equation?

thanks

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# I Differential Equations For Solving A Recursive equation

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