Further closed forms for finite sums of weighted products of the sine and cosine functions

Melham, RS

Further closed forms for finite sums of weighted products of the sine and cosine functions

Melham, RS

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Publication Type:: Journal Article
Citation:: Fibonacci Quarterly, 2018, 56 (1), pp. 38 - 42
Issue Date:: 2018-02-01

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Field	Value	Language
dc.contributor.author	Melham, RS	en_US
dc.date.issued	2018-02-01	en_US
dc.identifier.citation	Fibonacci Quarterly, 2018, 56 (1), pp. 38 - 42	en_US
dc.identifier.issn	0015-0517	en_US
dc.identifier.uri	http://hdl.handle.net/10453/133949
dc.description.abstract	© 2018 Fibonacci Association. All rights reserved. In this paper, we present closed forms for six families of finite sums of weighted products of the sine/cosine functions. In each finite sum that we define, the summand contains a product of trigonometric functions, and the length of this product can be made as large as we please. A special case of one of our main results is the sum i=1n2 cos12i cos i cos(i − 3) = cos 1 −cos n cos(n + 1) . 2n cosn 2 Here the weight term in the summand is2 cos12i.	en_US
dc.relation.ispartof	Fibonacci Quarterly	en_US
dc.subject.classification	General Mathematics	en_US
dc.title	Further closed forms for finite sums of weighted products of the sine and cosine functions	en_US
dc.type	Journal Article
utslib.citation.volume	1	en_US
utslib.citation.volume	56	en_US
utslib.for	0101 Pure Mathematics	en_US
utslib.for	0103 Numerical and Computational Mathematics	en_US
utslib.for	0199 Other Mathematical Sciences	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
utslib.copyright.status	open_access
pubs.issue	1	en_US
pubs.publication-status	Published	en_US
pubs.volume	56	en_US

Abstract:

© 2018 Fibonacci Association. All rights reserved. In this paper, we present closed forms for six families of finite sums of weighted products of the sine/cosine functions. In each finite sum that we define, the summand contains a product of trigonometric functions, and the length of this product can be made as large as we please. A special case of one of our main results is the sum i=1n2 cos12i cos i cos(i − 3) = cos 1 −cos n cos(n + 1) . 2n cosn 2 Here the weight term in the summand is2 cos12i.

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http://hdl.handle.net/10453/133949