Radius of Convergence of Power Series Expansion for Cosine Function/Mistake
Jump to navigation
Jump to search
Source Work
1960: Walter Ledermann: Complex Numbers:
- Chapter $4$: Elementary Functions of a Complex Variable:
- Section $4$: Power Series:
- Example $\text{(iii)}$
- Section $4$: Power Series:
This mistake can be seen in the $1960$ edition as published by Routledge & Kegan Paul.
Mistake
- The series $C \paren z = 1 - \dfrac {z^2} {2!} + \dfrac {z^4} {4!} - z \dfrac 6 {6!} + \cdots$ and $S \paren z = z - \dfrac {z^3} {3!} + \dfrac {z^5} {5!} - \dfrac {z^7} {7!} + \cdots$ also converge for all $z$, ...
Correction
The expression for $C \paren z$ should read $1 - \dfrac {z^2} {2!} + \dfrac {z^4} {4!} - \dfrac {z^6} {6!} + \cdots$
Sources
- 1960: Walter Ledermann: Complex Numbers ... (previous) ... (next): $\S 4.4$. Power Series: Example $\text {(iii)}$