# Thread:

1. ## period

Hey,

I'm trying to find the period of:

$f(x)=(\cos(\pi\gamma))^{n} \hspace{0,5cm}, \gamma \in \mathbb{R}, n \in \mathbb{N}$

It seems that when $n$ is even then the $f$ has period=1 and when $n$ is odd then $f$ has period=2 .

How to show that analytically?

2. As written, your function is not periodic. It's constant. Care to have another go?

3. ## period

Hey,

My mistake. It should say:

$<br /> f(x)=(\cos(\pi x))^{n} \hspace{0,5cm}, x \in \mathbb{R}, n \in \mathbb{N}$

4. Must you consider more than this?

$[cos(\pi x)]^{n+1} = [cos(\pi x)]^{n}\cdot cos(\pi x)$

If you can make conclusions about even values of n, there is not much left for odd values.

5. ## periodicity

Hey,

Sorry for the inconvenience. What I wanted do to was to arrive at the conclusion analytically rather than explanatory. How do I do that?

6. What's the definition of "Period"?

Something like: The minimum value of 'h' such that f(x+h) = f(x).

Definitions are always good places to start. They are not always the best places to start writing programs, but for proving results, they are gold.
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 7, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.9400900602340698, "perplexity_flag": "middle"}