The On-Line Encyclopedia of Integer Sequences (OEIS)

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A054374

Discriminant of Hermite polynomials.
(history; published version)

#34 by Charles R Greathouse IV at Sun Feb 16 08:32:42 EST 2025

LINKS

Eric Weisstein's World of Mathematics, <a href="httphttps://mathworld.wolfram.com/HermitePolynomial.html">Hermite Polynomial.</a>

Discussion

Sun Feb 16

08:32

OEIS Server: https://oeis.org/edit/global/3014

#33 by Vaclav Kotesovec at Thu Mar 02 08:08:51 EST 2023

STATUS

editing

approved

#32 by Vaclav Kotesovec at Thu Mar 02 08:08:46 EST 2023

FORMULA

a(n) ~ A * 2^(3*n*(n-1)/2) * n^(n*(n+1)/2 + 1/12) / exp(n^2/4), where A is the Glaisher-Kinkelin constant (see A074962). - Vaclav Kotesovec, Mar 02 2023

STATUS

approved

editing

#31 by Charles R Greathouse IV at Thu Sep 08 08:45:00 EDT 2022

PROG

(MAGMAMagma) [Round(2^(3*n*(n-1)/2)*(&*[j^j: j in [1..n]])): n in [1..8]]; // G. C. Greubel, Jun 10 2018

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#30 by Alois P. Heinz at Tue Sep 14 04:47:51 EDT 2021

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proposed

approved

#29 by Michel Marcus at Tue Sep 14 04:39:46 EDT 2021

STATUS

editing

proposed

#28 by Michel Marcus at Tue Sep 14 04:39:30 EDT 2021

COMMENTS

A054374 gives the discriminants of the Hermite polynomials in the conventional (physicists') normalization, and A002109 gives the discriminants of the Hermite polynomials in the (in my opinion more natural) probabilists' normalization. See refs Wikipedia and Szego eq. (6.71.7). - _Alan Sokal, _, Mar 02 2012

STATUS

approved

editing

Discussion

Tue Sep 14

04:39

Michel Marcus: user is registered

#27 by Susanna Cuyler at Tue Jun 12 10:22:01 EDT 2018

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proposed

approved

#26 by Michel Marcus at Tue Jun 12 03:09:11 EDT 2018

STATUS

editing

proposed

#25 by Michel Marcus at Tue Jun 12 03:09:07 EDT 2018

REFERENCES

Mohammad K. Azarian, On the Hyperfactorial Function, Hypertriangular Function, and the Discriminants of Certain Polynomials, International Journal of Pure and Applied Mathematics, Vol. 36, No. 2, 2007, pp. 251-257. Mathematical Reviews, MR2312537. Zentralblatt MATH, Zbl 1133.11012.

LINKS

Mohammad K. Azarian, <a href="http://www.ijpam.eu/contents/2007-36-2/9/9.pdf">On the Hyperfactorial Function, Hypertriangular Function, and the Discriminants of Certain Polynomials</a>, International Journal of Pure and Applied Mathematics, Vol. 36, No. 2, 2007, pp. 251-257. Mathematical Reviews, MR2312537. Zentralblatt MATH, Zbl 1133.11012.

STATUS

proposed

editing