Thursday, 14 January 2010

The book was reprinted, but some errata remain (updated on June 2014)

The book was reprinted and the errata in the previous post, among others, corrected.

But still, as expected, there is more:


1. Page 59, (3.35): the sentence after this equation should be changed to: ``where the primes indicates that the term with $T_0 (x)$ (only present for $n$ even) should be halved" (thanks to M. Lewis for the correction).

2. Page 66, (3.61): j = 0, should be k = 0,
(3.67): the index of the Chebyshev polynomial should be k

3. Page 67, line 1 below (3.68): (3.55) should be (3.60)
line 4 below (3.68): (3.60) should be (3.56).

4. Page 96, line 5, near the end of the line: "=0" should be deleted.

5. Page 99, lines 3 and 5 from the top: the parameter $\nu$ in the Coulomb
functions should be $\eta$ (four times).


6. Page 168, third paragraph: change "$w_0$ crosses" by "$z$ crosses" (twice)  (thanks to anonymous for the correction)

7. Page 145, 4 lines before algorithm 5.4: $\Gamma (\alpha+\beta+1)$ should be replaced by $\Gamma (\alpha+\beta+2)$.

8. Page 290, second paragraph, line one/two: read "polynomial of approximation".

9. Page 370. Eq. (12.60): the last term of the differential equations goes with minus sign.
The equation should read: $x^2 w''+ x w' -(x^2+n^2) w=0$

10. Formulas (9.60) - (9.62) should read, $L_{50}^{(0)}$ and not $L_{0}^{(50)}$ according to the definition on the page 287. And the same applies for the Weniger transform, $S_{50}^{(0)}$ and not $S_{0}^{(50)}$ (
thanks to aukie for the correction)

11. Theorem 4.17: the inequalities and the equality involving $a$ and $b$ should involve $|a|$ and $|b|$ instead.

12. The sentence "It is a straightforward... take place" in the proof of Theorem 4.17 should be deleted.

Wednesday, 13 January 2010

Complete list of errata found last year

The book was reprinted on 2009 and some errata corrected. Here is the list
of corrections:

*** Page 32, Eq. (2.90), last line: add parenthesis before the last bracket,
changing ``d_{n-1}(s,z_0]" to ``d_{n-1}(s,z_0)]"

*** Page 43, Eq. (2.140): the factor ``(-1)^k" should be deleted.

*** Page 84, line 10, change ``$\epsilon_0=\frac12$, $\epsilon_n=1\,(n\ge1)$"
to ``$\epsilon_0=1$, $\epsilon_n=2\,(n\ge1)$"

*** Page 84, line 12 (in the formula for A2), change ``z" to ``2z"

*** Page 121, two lines after (4.135): change ``the associated continued fraction"
by ``the associated homogeneous recurrence"

*** Page 136, line 7 from bottom: change ``second derivative"
to ``derivative $f^{(2n)}$"

*** Page 196, 1 line before (7.13): change ``I_0=[-\pi /2,\pi /2]"
to ``I_0=[0,\pi/2]"

*** Page 260, Eq. (8.117): in the second equation, the factor "dsp" should be
deleted (this is a Latex typesetting error).

*** Page 287, one line before (9.52): write "example, we can simply take $\zeta=1$ and"

Wednesday, 19 December 2007

Did you find an errata? Please, let us know

If you found an errata, we will be very thankful if you leave a comment.

So far, the following errata have been found (color codes: red for errata in formulas and blue for other errata or missprints):


  • Chap. 2

  • Page 43, Eq. (2.140): the factor (-1)^k should be deleted.
    (with thanks to Alfredo for pointing this out)


  • Chap. 4

  • Page 121, two lines after (4.135): "the associated CONTINUED FRACTION" should be replaced by "the associated HOMOGENEOUS RECURRENCE"


  • Chap. 8

  • Page 260, Eq. (8.117): in the second equation, the factor "dsp" should be deleted (LaTeX typesetting error).

    Thursday, 1 November 2007

    Sunday, 3 December 2006

    Software: the official link

    Software repository for the book here

    The BOOK: Numerical methods for special functions

    This is the blog associated to the book "Numerical Methods for Special Functions", by A. Gil, J. Segura and N.M. Temme, published by SIAM.