I don't know how to write the summation symbol so I'm providing you the original link to problem http://www.codechef.com/OCT11/problems/PARSIN .My approach to solve this problem is first reduce the expression sin(k1X) * sin(k2X) ..... *sin(kmX) to some terms where I can have k1+k2+....+km instead of their product.In doing so I don't need to find all possible combinations of (k1,k2,...,km).But not abled to do that.Can anyone please suggest any better ideas or at least tell me if I'm on a correct path or not ? For past three days I'm struggling with this problem and as my last hope I'm posting this problem here.Please help !!!!
Another Trigonometry problem, sum of products of sine function over partitions of N
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trigonometry
contest-math
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2Apparently you want [compositions](http://mathworld.wolfram.com/Composition.html), not partitions. – 2011-10-05
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0For the summation symbol, use \sum_{i=1}^k to get $\sum_{i=1}^k$ – 2011-10-05
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0Why don't you define the function recursively? Looking at the problem, this seems to me the natural thing to do. – 2011-10-05
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0@J.M. Compositions but how ? Are you applying composition for calculating sin(k1X)*sin(k2X)...*sin(kmX) ? Correct me if I'm wrong. – 2011-10-05
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0You might want to see [this book](http://www.math.upenn.edu/~wilf/website/CombAlgDownld.html), BTW... – 2011-10-05
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0@Raskolnikov How can we apply recursion for this.I have studied recursion which says you must have some base condition and some recursive formula for the function,but here I don't have those formula and conditions. – 2011-10-05
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0You can make a recursive formula since $f(M,N,X) = \sum_{k} f(1,k,X) f(M-1,N-k,X)$. – 2011-10-05
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0The summation symbol in TeX is \sum or \Sigma (capital S in the second one). I wrote the problem statement with TeX in the answer below. – 2011-10-05
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2$-1$:This is a problem from an ongoing contest in codechef.Discussing the solution now would be unfair.Please wait until the contest is over.Thanks. – 2011-10-05
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0yeah I think you are right but after struggling with the problem for so many days,I just can't resist myself from discussing the approach for this problem but I'll keep your suggestion in mind. – 2011-10-06