Dmytro Boiko
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- Joined
- Jul 28, 2020
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I have a functional series of this kind
[MATH]f(x) = \sum_{n=0}^{\infty} \cfrac{1}{\sqrt{s^2 + l^2(2 n + 1 + (-1)^n x)^2}}[/MATH]During the study there is an assumption about the periodicity
[MATH]f(x) = f(x + 4k), \quad k \in \mathbb{Z} [/MATH]The amplitude varies within
[MATH]m_1= \sum_{n=0}^{\infty} \cfrac{1}{\sqrt{s^2 + l^2(2 n + 1 + (-1)^n)^2}}[/MATH][MATH]m_2 = \sum_{n=0}^{\infty} \cfrac{1}{\sqrt{s^2 + l^2(2 n + 1 - (-1)^n)^2}}[/MATH]
Has anyone encountered functions of this kind?
How can you prove the periodicity?
Is it possible to find another species without using a series?
Thank you very much, I'm sorry if not in that topic.
[MATH]f(x) = \sum_{n=0}^{\infty} \cfrac{1}{\sqrt{s^2 + l^2(2 n + 1 + (-1)^n x)^2}}[/MATH]During the study there is an assumption about the periodicity
[MATH]f(x) = f(x + 4k), \quad k \in \mathbb{Z} [/MATH]The amplitude varies within
[MATH]m_1= \sum_{n=0}^{\infty} \cfrac{1}{\sqrt{s^2 + l^2(2 n + 1 + (-1)^n)^2}}[/MATH][MATH]m_2 = \sum_{n=0}^{\infty} \cfrac{1}{\sqrt{s^2 + l^2(2 n + 1 - (-1)^n)^2}}[/MATH]
Has anyone encountered functions of this kind?
How can you prove the periodicity?
Is it possible to find another species without using a series?
Thank you very much, I'm sorry if not in that topic.