The Maclaurin series for f(x)= $\frac{\sinh(x)}{\x}$

asked by guest
on Nov 15, 2024 at 2:34 pm



You asked:

Find the Maclaurin series of the function \(f\left( x \right) = \frac{\sinh\left( x \right)}{x}\).

MathBot Answer:

Series expansion:

\[1 + \frac{x^{2}}{6} + \frac{x^{4}}{120} + \frac{x^{6}}{5040} + \frac{x^{8}}{362880} + \frac{x^{10}}{39916800}+ \cdots\]


Series representation:

\[\frac{\sum_{n=0}^{\infty} \frac{x^{2 n + 1}}{\left(2 n + 1\right)!}}{x}\]