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Integer Sequences for the Sum of Powers of Trigonometric Values

DOI: 10.4236/oalib.1105417, PP. 1-41

Subject Areas: Mathematical Analysis

Keywords: Integer Sequence, Heptagonal Triangle, Sine, Cosine, Tangent, Recurrence Equation

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Abstract

We will develop some methods to generate integer sequences whose terms are sums of mixed powers of trigonometric values at angles of a heptagonal triangle. Our method will produce many new integer sequences and reproduce some sequences which are discovered using different methods by other researchers.

Cite this paper

Wang, K. (2019). Integer Sequences for the Sum of Powers of Trigonometric Values. Open Access Library Journal, 6, e5417. doi: http://dx.doi.org/10.4236/oalib.1105417.

References

[1]  Witula, R. (2009) Type Trigonometric Formulas: The General Form for the Argument 2π/7. Journal of Integer Sequences, 12, 1-23.
[2]  Berndt, B.C. and Zhang, L.C. (1992) Ramanujans Identities for Eta-Functions. Mathematische Annalen, 292, 561-573 https://doi.org/10.1007/BF01444636
[3]  Wang, K. (2016) Sums of Mixed Trigonometric Powers.
[4]  Bankoff, L. and Garfunkel, J. (1973) The Heptagonal Triangle. Mathematics Magazine, 46, 7-19. https://doi.org/10.1080/0025570X.1973.11976267
[5]  WIKI. Heptagonal Triangle. https://en.wikipedia.org/wiki/Heptagonal_triangle
[6]  OIES The On-Line Encyclopedia of Integer Sequences.
https://oeis.org/wiki/Welcome

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