Basic trigonometric power sums with applications. (English) Zbl 1357.33003
Summary: We present the transformation of several sums of positive integer powers of the sine and cosine into non-trigonometric combinatorial forms. The results are applied to the derivation of generating functions and to the number of the closed walks on a path and in a cycle.
MSC:
| 33B10 | Exponential and trigonometric functions |
| 05A15 | Exact enumeration problems, generating functions |
| 11B65 | Binomial coefficients; factorials; \(q\)-identities |
Keywords:
basic trigonometric power sum; binomial coefficient; closed walk; cosine; cycle; generating function; graph; path; sineOnline Encyclopedia of Integer Sequences:
Triangle version of the array of the number of closed paths of even length on the graph P_n (n vertices, n-1 edges).References:
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