Re: don't toss your circa 1964 Abramowitz and Stegun just yet.

Raymond Toy <[email protected]> Sat, 11 Jul 2026 07:10:44 -0700
Newsgroups	gmane.comp.mathematics.maxima.general
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On 7/11/26 6:27 AM, Barton Willis via Maxima-discuss wrote:

> Table 22.7 (page 782) of Abramowitz and Stegun (1964) gives the 
> order-only recursion for the Jacobi polynomials.  This recursion is 
> missing from Table 18.9.1 
> <https://dlmf.nist.gov/18.9><https://dlmf.nist.gov/18.9>of the DLMF.  
> Later, the DLMF gives several Jacobi polynomial recursions that 
> involve the parameters and the order. 
> <http://dlmf.nist.gov/18.9.E4><http://dlmf.nist.gov/18.9.E4>  I didn't 
> try, but possibly these recursions imply the order-only recursion.
>
> Lesson:  Unless you are eager to do some tedious linear algebra, don't 
> toss your 62 year old Abramowitz and Stegun just yet.
Heh. I haven’t opened my copy in a long time since I tend to use the 
online pdf versions such as 
https://personal.math.ubc.ca/~cbm/aands/abramowitz_and_stegun.pdf. There 
are others around.

We should probably add some references to our manual to link to DLMF 
and/or A&S, like we do for other functions.

>
> --Barton
>
>
> _______________________________________________
> Maxima-discuss mailing list
> [email protected]
> https://lists.sourceforge.net/lists/listinfo/maxima-discuss
&#8203;
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    <div class=3D"markdown-here-wrapper">
      <p style=3D"margin-bottom: 19.2px; margin-top: 0px;">On 7/11/26 6:2=
7
        AM, Barton Willis via Maxima-discuss wrote:<br>
      </p>
      <blockquote type=3D"cite"
style=3D"border-block-color: rgb(119, 119, 119); border-bottom-color: rgb=
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19); padding-inline: 16px; padding-left: 16px; padding-right: 16px; quote=
s: none; text-decoration-color: rgb(119, 119, 119); text-emphasis-color: =
rgb(119, 119, 119);">
        <style type=3D"text/css" style=3D"display:none;"> P {margin-top:0=
;margin-bottom:0;} </style>
        <div class=3D"elementToProof"
style=3D"font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Cal=
ibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
          Table 22.7 (page 782) of Abramowitz and Stegun (1964) gives
          the order-only recursion for the Jacobi polynomials.=C2=A0 This=

          recursion is missing from
          <a href=3D"https://dlmf.nist.gov/18.9"
            id=3D"OWA0455660e-3613-2927-a08d-cac1630b091f"
            class=3D"OWAAutoLink" title=3D"https://dlmf.nist.gov/18.9">
            Table 18.9.1</a><a href=3D"https://dlmf.nist.gov/18.9"
            id=3D"OWA99e3ad06-aa25-71ea-8930-2d1edcfc617c"
            class=3D"OWAAutoLink" title=3D"https://dlmf.nist.gov/18.9"
            style=3D"text-decoration: none;">
          </a>of the DLMF.=C2=A0 Later, the DLMF gives several Jacobi
          polynomial recursions that involve the
          <a href=3D"http://dlmf.nist.gov/18.9.E4"
            id=3D"OWA1a4263f9-0ad6-fa9d-7fb6-8412ca986ca4"
            class=3D"OWAAutoLink" title=3D"http://dlmf.nist.gov/18.9.E4">=

            parameters and the order.</a><a
            href=3D"http://dlmf.nist.gov/18.9.E4"
            id=3D"OWA194a4d83-bdbf-e49a-b3ea-a1b24d040eaa"
            class=3D"OWAAutoLink" title=3D"http://dlmf.nist.gov/18.9.E4"
            style=3D"text-decoration: none;">=C2=A0</a>=C2=A0 I didn't tr=
y, but
          possibly these recursions imply the order-only recursion.</div>=

        <div class=3D"elementToProof"
style=3D"font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Cal=
ibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
          <br>
        </div>
        <div class=3D"elementToProof"
style=3D"font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Cal=
ibri, Helvetica, sans-serif; font-size: 12pt;">
          <span style=3D"color: rgb(0, 0, 0);">Lesson:=C2=A0 Unless you a=
re
            eager to do some tedious linear algebra, don't toss your 62
            year old
          </span><span style=3D"color: rgb(0, 0, 0);">Abramowitz and
            Stegun just yet.=C2=A0</span></div>
      </blockquote>
      Heh. I haven=E2=80=99t opened my copy in a long time since I tend t=
o use
      the online pdf versions such as <a
href=3D"https://personal.math.ubc.ca/~cbm/aands/abramowitz_and_stegun.pdf=
"
        class=3D"moz-txt-link-freetext">https://personal.math.ubc.ca/~cbm=
/aands/abramowitz_and_stegun.pdf</a>.
      There are others around.
      <p style=3D"margin-bottom: 19.2px; margin-top: 0px;">We should
        probably add some references to our manual to link to DLMF
        and/or A&amp;S, like we do for other functions.</p>
      <blockquote type=3D"cite"
style=3D"border-block-color: rgb(119, 119, 119); border-bottom-color: rgb=
(119, 119, 119); border-inline-color: rgb(114, 159, 207) rgb(119, 119, 11=
9); border-inline-start: 2px solid rgb(114, 159, 207); border-left: 2px s=
olid rgb(114, 159, 207); border-right-color: rgb(119, 119, 119); border-t=
op-color: rgb(119, 119, 119); color: rgb(119, 119, 119); column-rule-colo=
r: rgb(119, 119, 119); margin: 19.2px 0px; outline-color: rgb(119, 119, 1=
19); padding-inline: 16px; padding-left: 16px; padding-right: 16px; quote=
s: none; text-decoration-color: rgb(119, 119, 119); text-emphasis-color: =
rgb(119, 119, 119);">
        <div class=3D"elementToProof"
style=3D"font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Cal=
ibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
          <br>
        </div>
        <div class=3D"elementToProof"
style=3D"font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Cal=
ibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
          --Barton</div>
        <br>
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        <br>
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        <pre wrap=3D"" class=3D"moz-quote-pre">__________________________=
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