Power Series Expansion for Tangent Function/Mistake

Source Work

1992: George F. Simmons: Calculus Gems:

Chapter $\text {B}.20$: The Bernoulli Numbers and some Wonderful Discoveries of Euler

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 [ Power 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 Power Series Expansion for Tangent Function/Sequence.

Also see

• Power Series Expansion for Tangent Function

Sources

• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {B}.20$: The Bernoulli Numbers and some Wonderful Discoveries of Euler