The Maclaurin series for f(x)=xcosh($x^{2}$ )

asked by guest
on Nov 15, 2024 at 2:36 pm



You asked:

Find the Maclaurin series of the function \(f\left( x \right) = x \cdot \cosh\left( {x}^{2} \right)\).

MathBot Answer:

Series expansion:

\[x + \frac{x^{5}}{2} + \frac{x^{9}}{24} + \frac{x^{13}}{720} + \frac{x^{17}}{40320} + \frac{x^{21}}{3628800}+ \cdots\]


Series representation:

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