Power Series Expansion for Real Area Hyperbolic Cosine/Mistake

Source Work

1976: K. Weltner and W.J. Weber: Mathematics for Engineers and Scientists

$8$. Taylor Series and Power Series:

Appendix: Table $8.2$: Power Series of Important Functions

Mistake

$\cosh^{-1} x = \paren {\ln 2} x - \dfrac 1 {\paren {2 \times 2} x^2} - \dfrac {1 \times 3} {\paren {2 \times 4 \times 4} x^4} - \dfrac {1 \times 3 \times 5} {\paren {2 \times 4 \times 6 \times 6} x^6} - \cdots \quad \paren {x \ge 1}$

Correction

The first term should read $\map \ln {2 x}$.

Hence the formula should be:

$\cosh^{-1} x = \map \ln {2 x} - \dfrac 1 {\paren {2 \times 2} x^2} - \dfrac {1 \times 3} {\paren {2 \times 4 \times 4} x^4} - \dfrac {1 \times 3 \times 5} {\paren {2 \times 4 \times 6 \times 6} x^6} - \cdots$

Sources

• 1976: K. Weltner and W.J. Weber: Mathematics for Engineers and Scientists ... (previous) ... (next): $8$. Taylor Series and Power Series: Appendix: Table $8.2$: Power Series of Important Functions