Power Series Expansion for Tangent Function/Mistake

Source Work

 * Chapter $\text {B}.20$: The Bernoulli Numbers and some Wonderful Discoveries of Euler
 * The Power Series for the Tangent
 * The Power Series for the Tangent

This mistake can be seen in the $1992$ edition as published by McGraw-Hill: ISBN 0-07-057566-5

Mistake

 * "Based on our knowledge of the Bernoulli numbers, the first few terms of the [ Taylor Series Expansion for Tangent Function ] are easy to calculate explicitly,


 * $\tan x = x + \dfrac 1 3 x^3 + \dfrac 2 {15} x^5 + \dfrac {17} {315} x^7 + \dfrac {67} {2835} x^9 + \cdots$"

The numerator of the coefficient for $x^9$ is in fact $62$, not $67$.

The correct calculation can be found in Taylor Series Expansion for Tangent Function/Sequence.

Also see

 * Taylor Series Expansion for Tangent Function