Maclaurin series for sin p with p an integer greater than 2

Date

2018-07-01

Authors

Kotrla, Lukas

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

We find an explicit formula for the coefficients of the generalized Maclaurin series for sin p provided p > 2 is an integer. Our method is based on an expression of the n-th derivative of sin p in the form ∑2n-2-1k=0 αk,n sin p-1 p(x) cos2-pp(x), x ∈ (0, πp/2), where cos p stands for the first derivative of sin p. The formula allows us to compute the nonzero coefficients. α n = lim x→0+ sin(np+1)p(x)/(np + 1)!

Description

Keywords

p-Laplacian, p-Trigonometry, Approximation, Analytic function coefficients of Maclaurin series

Citation

Kotrla, L. (2018). Maclaurin series for sin p with p an integer greater than 2. Electronic Journal of Differential Equations, 2018(135), pp. 1-11.

Rights

Attribution 4.0 International

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