On Some Trigonometric Power Sums
نویسنده
چکیده
In contrast to Fourier series, these finite power sums are over the angles equally dividing the upper-half plane. Moreover, these beautiful and somewhat surprising sums often arise in analysis. In this note, we extend the above results to the power sums as shown in identities (17), (19), (25), (26), (32), (33), (34), (35), and (36) and in the appendix. The method is based on the generating functions. To begin, we establish two auxiliary trigonometric identities, derived from the Chebyshev polynomial of the second kind. Let Un(x) be the Chebyshev polynomial of the second kind [3, pages 7–10]
منابع مشابه
A Few Finite Trigonometric Sums
Finite trigonometric sums occur in various branches of physics, mathematics, and their applications. These sums may contain various powers of one or more trigonometric functions. Sums with one trigonometric function are known; however, sums with products of trigonometric functions can become complicated, and may not have a simple expression in a number of cases. Some of these sums have interest...
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