List questions from recurrence-relations

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Finding a reduction formula for this integral

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Proof that $\forall x \in \mathbb{R}, \forall n \in \mathbb{N}: (f(x))^n = f(nx)$ only has solutions of the form $f(x) = c^x$ for some constant $c$

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A sequence was defined by a equation

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Find the general term of the recursive relation $a_{n+1}=\frac{1}{n+1}\sum\limits_{k=0}^n a_k 2^{2n-2k+1}$

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How do I find $f(4)$ when $f(n)= f(n-1)+ 2n$?

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Integral involving the spherical Bessel function of the first kind: $\int_{0}^{\infty} x^{-n}j_{n+1}(x) \, dx$

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Show that $2^n(\cos^n(\frac{2\pi}{9})+\cos^n(\frac{4\pi}{9})+\cos^n(\frac{8\pi}{9}))\in\mathbb{Z}$

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How to really solve a non-homogeneous recurrence

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Solving a recursion relation: $a_{n+1}=-3a_n+4a_{n-1}+2$

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Stirling number of the second kind recurrence relations

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Is there a standard recurrence relation to solve this?

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Particular solution of recurrence relation

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Finding an exact solution to a difference equation

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Divide and Conquer Recurrence Relation help?

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List Question

First order recurrence relation

Finding a reduction formula for this integral

Proof that $\forall x \in \mathbb{R}, \forall n \in \mathbb{N}: (f(x))^n = f(nx)$ only has solutions of the form $f(x) = c^x$ for some constant $c$

A sequence was defined by a equation

Find the general term of the recursive relation $a_{n+1}=\frac{1}{n+1}\sum\limits_{k=0}^n a_k 2^{2n-2k+1}$

How do I find $f(4)$ when $f(n)= f(n-1)+ 2n$?

Integral involving the spherical Bessel function of the first kind: $\int_{0}^{\infty} x^{-n}j_{n+1}(x) \, dx$

Show that $2^n(\cos^n(\frac{2\pi}{9})+\cos^n(\frac{4\pi}{9})+\cos^n(\frac{8\pi}{9}))\in\mathbb{Z}$

How to really solve a non-homogeneous recurrence

Solving a recursion relation: $a_{n+1}=-3a_n+4a_{n-1}+2$

Stirling number of the second kind recurrence relations

Is there a standard recurrence relation to solve this?

Particular solution of recurrence relation

Finding an exact solution to a difference equation

Divide and Conquer Recurrence Relation help?

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