On generalized trigonometric functions and series of rational functions

Han Yu

doi:10.1016/J.jnt.2017.05.015

On generalized trigonometric functions and series of rational functions

Han Yu

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Here we introduce a way to construct generalized trigonometric functions associated with any complex polynomials. The well known trigonometric functions can be seen to be associated with polynomial x² - 1 . We will show that those generalized trigonometric functions have algebraic identities which generalizes the well known sin²(x) + cos²(x) = 1 . One application of the generalized trigonometric functions is in evaluating infinite series of rational functions.

Original language	English
Pages (from-to)	512-532
Journal	Journal of Number Theory
Volume	180
Early online date	14 Jul 2017
DOIs	https://doi.org/10.1016/J.jnt.2017.05.015
Publication status	Published - Nov 2017

Keywords

Infinite series
Rational functions
Generalized trigonometric functions

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title = "On generalized trigonometric functions and series of rational functions",

abstract = "Here we introduce a way to construct generalized trigonometric functions associated with any complex polynomials. The well known trigonometric functions can be seen to be associated with polynomial x2 - 1 . We will show that those generalized trigonometric functions have algebraic identities which generalizes the well known sin2(x) + cos2(x) = 1 . One application of the generalized trigonometric functions is in evaluating infinite series of rational functions.",

keywords = "Infinite series, Rational functions, Generalized trigonometric functions",

author = "Han Yu",

year = "2017",

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doi = "10.1016/J.jnt.2017.05.015",

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AU - Yu, Han

PY - 2017/11

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N2 - Here we introduce a way to construct generalized trigonometric functions associated with any complex polynomials. The well known trigonometric functions can be seen to be associated with polynomial x2 - 1 . We will show that those generalized trigonometric functions have algebraic identities which generalizes the well known sin2(x) + cos2(x) = 1 . One application of the generalized trigonometric functions is in evaluating infinite series of rational functions.

AB - Here we introduce a way to construct generalized trigonometric functions associated with any complex polynomials. The well known trigonometric functions can be seen to be associated with polynomial x2 - 1 . We will show that those generalized trigonometric functions have algebraic identities which generalizes the well known sin2(x) + cos2(x) = 1 . One application of the generalized trigonometric functions is in evaluating infinite series of rational functions.

KW - Infinite series

KW - Rational functions

KW - Generalized trigonometric functions

UR - https://www.scopus.com/pages/publications/85024495789

U2 - 10.1016/J.jnt.2017.05.015

DO - 10.1016/J.jnt.2017.05.015

M3 - Article

SN - 0022-314X

VL - 180

SP - 512

EP - 532

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

On generalized trigonometric functions and series of rational functions

Abstract

Keywords

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