The result of ∑(p-i)cos(iθ) ?

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Roshdy

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solve this formula

Dear all
I need the result of this formula

∑(p-i)cos(iθ) ,

p is a constant, i is the index run from 1 to (p-1)
 

solve this formula

By MathCAD's equation solver (with rearrangement) ...

( (1-cos(pΘ))-p(1-cos(Θ)) ) / ( 2(1-cos(Θ)) )


I'll try to verify this later, but my guess is that it's correct

Added after 4 hours 47 minutes:

That solution (numerically) holds well for Theta > 0,
but has severe problems as Theta-->0.

I'm am out of town - I welcome another's help.

If nothing else, I will put actual analytical time into this when I can. (sadly, it just can't be today)
 

    Roshdy

    Points: 2
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solve this formula

I was wrong - the solution is correct -
the "discontinuity" I noticed is only when theta=0, which is undefined in the solution I provided.

L'Hopital shows this singular point as (p^2 - p) / 2,
which is the same as that of the summation.

My worries were unfounded,
( (1-cos(pΘ))-p(1-cos(Θ)) ) / ( 2(1-cos(Θ)) )
is the answer.

 

    Roshdy

    Points: 2
    Helpful Answer Positive Rating
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