don't toss your circa 1964 Abra mowitz and Stegun just yet.
Barton Willis via Maxima-discuss <[email protected]> Sat, 11 Jul 2026 13:27:42 +0000
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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 DLM=
F. Later, the DLMF gives several Jacobi polynomial recursions that involve=
the parameters and the order.<http://dlmf.nist.gov/18.9.E4> <http://dlmf.n=
ist.gov/18.9.E4> I didn't try, but possibly these recursions imply the or=
der-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.
--Barton
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Table 22.7 (page 782) of Abramowitz and Stegun (1964) gives the order-only =
recursion for the Jacobi polynomials. This recursion is missing from
<a href=3D"https://dlmf.nist.gov/18.9" id=3D"OWA0455660e-3613-2927-a08d-cac=
1630b091f" 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-aa=
25-71ea-8930-2d1edcfc617c" class=3D"OWAAutoLink" title=3D"https://dlmf.nist=
.gov/18.9" style=3D"text-decoration: none;">
</a>of the DLMF. Later, the DLMF gives several Jacobi polynomial recu=
rsions that involve the
<a href=3D"http://dlmf.nist.gov/18.9.E4" id=3D"OWA1a4263f9-0ad6-fa9d-7fb6-8=
412ca986ca4" 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"ht=
tp://dlmf.nist.gov/18.9.E4" style=3D"text-decoration: none;"> </a>&nbs=
p; I didn't try, but possibly these recursions imply
the order-only recursion.</div>
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<br>
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nt, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt;">
<span style=3D"color: rgb(0, 0, 0);">Lesson: Unless you are 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.=
</span></div>
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<br>
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olor: rgb(0, 0, 0);">
--Barton</div>
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