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. <i>Electronic Journal of Differential Equations, 2018</i>(135), pp. 1-11.
Rights
Attribution 4.0 International