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Subject: "simplification of a sine series"     Previous Topic | Next Topic
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Conferences The CTK Exchange College math Topic #446
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bmclean
Member since Apr-20-04
Apr-20-04, 09:11 PM (EST)
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"simplification of a sine series"
 
   I am familiar with the trig identity

sum{n=0->N} sin(nx) = {sin(Nx/2).sin((N+1)x/2)}/sin(x/2)

that is,

derived via exponential sums (see https://mathworld.wolfram.com/Sine.html formulas (11) to (15)).

In my research (geophysics) I could really make use of a similar simplification if one can be derived, for the slightly more complicated sine series

sum{n=0->N} p_n.sin(q.n.x+r_n)
where p_n is a set of N+1 real numbers
q is a real number
r_n is a set of N+1 real numbers

that is,

I do not know if this is possible. If it is, it may bring a new technique into the realms of being computationally achievable! We shall see. Simplifications of the above kind, or any alternate ideas would be gratefully received, or even qualified statements as to why this isnt going to be simplified would be helpful.

Thanks,
Ben.

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bmclean
Member since Apr-20-04
Apr-21-04, 08:15 AM (EST)
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1. "RE: simplification of a sine series"
In response to message #0
 
   Heres some work so far, actually it went a lot further before I showed myself the inequality in equation (g) :(

I post it at the risk of narrowing creativity by suggesting people think like me... please feel free to think along entirely different lines.

Ben.

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