Matematické Fórum

stuart clark

Let $\displaystyle \int_0^x 2xf^2(t)\;dt=\left( \int_0^x 2f(x-t)\;dt \right)^2, \quad f(1)=1$

function $f(x)$ is continuous for $x>0$ and $\{a_n\}$ is a sequence such that

$a_{n+1}=a_n+\sqrt{1+a_n^2}$ for $a_0=0$ .

If $f(x)$ is an increasing function, then $\lim_{n\to \infty} \frac{a_k}{2^{n-1}}$ where $k=f(n^{\sqrt{2}-1})$

vanok · 11. 07. 2018 18:00

Hi ↑ stuart clark:,
See https://math.stackexchange.com/question … 11#2844111

Matematické Fórum

#1 07. 07. 2018 08:40 — Editoval stuart clark (07. 07. 2018 08:41)

Functional equation

#2 11. 07. 2018 18:00

Re: Functional equation

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