Consider the relation

$t_{k}(n) = 2 t_{k-1}(frac{n}{2}) + f(n)$

Where $t_{0}(n) = x^p$ and $f(n)=alpha n^q$.

How can I get an arbitrary element $t_{k}(n)$ for example with $p=2,q=1,alpha=1$ using Mathematica syntax?

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# How to define this recursive function?

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Consider the relation

$t_{k}(n) = 2 t_{k-1}(frac{n}{2}) + f(n)$

Where $t_{0}(n) = x^p$ and $f(n)=alpha n^q$.

How can I get an arbitrary element $t_{k}(n)$ for example with $p=2,q=1,alpha=1$ using Mathematica syntax?

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