Max of sum of sines

  • Thread starter ekkilop
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  • #1
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Hi!

Consider the function

[itex] \frac{d^n}{dx^n} \sum_{k=1}^m \sin{kx}, \quad 0 \leq x \leq \pi/2 [/itex].

If [itex] n [/itex] is odd this function attains its largest value, [itex] \sum_{k=1}^m k^n [/itex] at [itex] x=0 [/itex]. But what about if [itex] n [/itex] is even? Where does the maximum occur and what value does it take?

Any help is much appreciated. Thank you!
 
Last edited:

Answers and Replies

  • #2
Simon Bridge
Science Advisor
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Please make some attempt at the problem when you ask for help.
i.e. how would you normally go about finding the maximum?
Can you prove the statement about when m is odd?
 

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