Search results:
334.
$a^x = 1 + x\,\ln a + \dfrac{(x\,\ln a)^2}{2!} + \dfrac{(x\,\ln a)^3}{3!} + \cdots$
335.
$\ln(1+x) = x - \dfrac{x^2}{2} + \dfrac{x^3}{3} - \dfrac{x^4}{4} + \cdots \quad -1 < x \leq 1$
338.
$\arcsin x = x + \dfrac{1}{2}\dfrac{x^3}{3} + \dfrac{1 \cdot 3}{2 \cdot 4} \frac{x^5}{5} + \dfrac{1\cdot3\cdot5}{2\cdot4\cdot6}\frac{x^7}{7} + \cdots \quad -1 < x <1$
339.
$\coth x = \dfrac{1}{x} + \dfrac{x}{3} - \dfrac{x^3}{45} + \cdots \dfrac{(-1)^{n-1} 2^{2n}B_nx^{2n-1}}{(2n)!} + \cdots \quad 0 < |x| < \pi$
340.
$\tanh x = x - \dfrac{x^3}{3} + \dfrac{2x^5}{15} + \cdots \dfrac{(-1)^{n-1} 2^{2n}\left(2^{2n}-1\right)B_nx^{2n-1}}{(2n)!} + \cdots \quad |x| < \frac{\pi}{2}$