# Errata

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## Errata.

Please see this list for the errata reported before June 2010. Here are the errata that have been reported since November 2011. For brevity, we have suppressed the spelling and grammatical errors. This list is for errors in the text. Errors in web content are just fixed when reported; errata in lectures are listed here.

• 9. Coefficient in third term on line 5 should be 1/12 (Steve Kroon 10/4/13)

• 47. Replace $z^{r+2}$ by $z^{r+1}$ in Figure I.9 (Jonathan Woodworth, 12/19/11)

• 85. The formula for the example $Z(S_m)$ is wrong in Note I.58 (it should be a polynomial), so add the constraint $j_1+2j_2+\dots+mj_m=m$ to the sum (Bruno Salvy, 5/25/13)

• 86. Last line of Note I.60 needs recasting (especially fonts) (Bruno Salvy, 5/25/13)

• 87. Formal definition of substitution would translate to $B(zC(z))$ and is incorrect. Should be $$\sum_{k\geq 0} \sum\limits_{\beta \in \mathcal B_k}\epsilon_{\beta} \times \hbox{ Suc}_{k}(\mathcal C)$$ where each $\epsilon_\beta$ is a neutral class $\forall \ \beta \in \mathcal B$. (Ricardo Gomez, 9/17/13)

• 113. Entry for $k=2$ in the table should be $6.22\times 10^{-56}$ (David Daniels, 7/22/13)

• 160. $k$ should be $\ell$ and $\ell$ should be only $y\sqrt{\nu/2}$ when taking the limit in Note III.3 (Bruno Salvy, 5/25/13)

• 246. Better to specify the restriction that $f(z)$ has nonnegative real coefficients (David Daniels, 9/11/13)

• 256. $\alpha_1^{-n+r}$ should be $\alpha_1^{-n-r}$ on line -4 (David Daniels, 9/10/13)

• 295. $n/2$ -> $n/4$ and $n/4$ -> $n/8$ on line 21 (Antonio Vera, 5/25/13)

• 338. Replace $z_m$ by $z_1$ and $z_m$ by $z_2$ in the first two columns of the bottom row in the determinant in V.27 (Mark Sellke, 12/5/11)

• 338. Replace $z_i$ by $z_j$ at the end of the last line (Mark Sellke, 12/5/11)

• 390. Thm VI.3 is stated for real $\alpha$ and $\beta$, but that assumption should be explicit in Cor VI.1 too (Bruno Salvy, 5/25/13)

• 446. $\Gamma(s)$ -> $\log\Gamma(s)$ on line -4 (Bruno Salvy, 5/25/13)

• 448. "G" -> "K" on last line of the page (two instances) (Antonio Vera, 12/22/13)

• 475. Replace $Y_{2n-1}$ by ${1\over 2}Y_{2n-1}$ on line 3 (Mark Ward 5/7/12)

• 475. Replace 4 by $2^{7/4}$ on line 3 (Alex Daifotis, Nader Al-Naji, and Mark Ward 5/7/12)

• 533. $K_r$ -> $\Lambda_r$ in (145) (Bruno Salvy, 5/25/13)

• 534. $3r-1$ -> $3r-4$ in (146) (Bruno Salvy, 5/25/13)

• 605. Replace 2 by $\sqrt3/(2\pi)$ in Proposition VIII.11 (Svante Janson, 11/14/11)

• 625.$\frac{1}{2\pi T}$ -> $\frac{\pi}{2T}$ in (11) since the constant is $$\frac{1}{2\pi} \int_{T\leq |t| \leq \pi} \frac{1}{|1-e^{it}|} dt \leq \frac{1}{2\pi} \int_{T\leq |t| \leq \pi} \frac{\pi}{2 |t|} \leq \frac{1}{4T} 2(\pi-T) \leq \frac{\pi}{2T}$$ (Daniel Krenn, 2/7/13)

• 630. $g'(u_0 \tau_h)$ -> $\frac{u_0 g'(u_0 \tau_h)}{g'(\tau_h)}$ on line -15 (Daniel Krenn, 2/7/13)

• 657. Equation (39): Second term should have a factor of 2. (Clemens Heuberger, 8/16/12)

• 657. Equation (40): First term should be negated. (Clemens Heuberger, 8/16/12)

• 657. Equation after (41): First term should be negated. (Clemens Heuberger, 8/16/12)

• 668. The outer arc is $\gamma_3$ and the linear parts are $\gamma_2$ and $\gamma4$ in lines 19--20 (Daniel Krenn, 2/7/13)

• 668. $-1+n\Delta$ -> $n(\gamma-1)$ on line 22 (Daniel Krenn, 2/7/13)

• 668. "decrease continuously from" -> "varies continuously between" on line 25 (Daniel Krenn, 2/7/13)

• 668. Add constant factor $K$ to RHS of inequality on line -1 (Daniel Krenn, 2/7/13)

• 670. $A<\alpha(1)+1/2$ on line 9, so $\alpha(1)\in\mathbb{R}$ should be assumed (at least in Theorem IX.11 on page 669) (Daniel Krenn, 2/7/13)

• 682. $(z,u)=(\rho,\tau)$ -> $(z,\tau)=(\rho,1)$ on line 23 (Daniel Krenn, 2/7/13)

• 686.The notation used for the falling factorials, e.g. $(\alpha)_{(r)}$, is inconsistent with the falling factorials defined on p. 520 where they look like $\theta^{\underline{\ell}}$ (Daniel Krenn, 2/7/13)

• 686. $n$ missing under $\sup$ on line 9 (Daniel Krenn, 2/7/13)

• 712. $\cal M$ -> $\cal F$ on line 17 (Daniel Krenn, 2/7/13)

• 712. $r_H$ -> $\rho_H$ and $r_G$ -> $\rho_G$ on line 21 (Daniel Krenn, 2/7/13)

• 738. Replace 1 by the empty class in the pruned binary tree speficiation. (Antonio Vera, 4/5/13)

• 741. Interchange the exponents l and m on line 4 (Tom Hillegers, 5/7/12)

• 752. "height" -> "width" on line -9 (Antonio Vera, 4/5/13)