Hermite polynomials (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Hermite polynomials" in English language version.

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Tom H. Koornwinder, Roderick S. C. Wong, and Roelof Koekoek et al. (2010) and Abramowitz & Stegun. Koornwinder, Tom H.; Wong, Roderick S. C.; Koekoek, Roelof; Swarttouw, René F. (2010), "Orthogonal Polynomials", in Olver, Frank W. J.; Lozier, Daniel M.; Boisvert, Ronald F.; Clark, Charles W. (eds.), NIST Handbook of Mathematical Functions, Cambridge University Press, ISBN 978-0-521-19225-5, MR 2723248.
Abramowitz & Stegun 1983, p. 508–510, 13.6.38 and 13.5.16. Abramowitz, Milton; Stegun, Irene Ann, eds. (1983) [June 1964]. "Chapter 22". Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Applied Mathematics Series. Vol. 55 (Ninth reprint with additional corrections of tenth original printing with corrections (December 1972); first ed.). Washington D.C.; New York: United States Department of Commerce, National Bureau of Standards; Dover Publications. p. 773. ISBN 978-0-486-61272-0. LCCN 64-60036. MR 0167642. LCCN 65-12253.
Indritz, Jack (1961), "An inequality for Hermite polynomials", Proceedings of the American Mathematical Society, 12 (6): 981–983, doi:10.1090/S0002-9939-1961-0132852-2, MR 0132852
Banderier, Cyril; Bousquet-Mélou, Mireille; Denise, Alain; Flajolet, Philippe; Gardy, Danièle; Gouyou-Beauchamps, Dominique (2002), "Generating functions for generating trees", Discrete Mathematics, 246 (1–3): 29–55, arXiv:math/0411250, doi:10.1016/S0012-365X(01)00250-3, MR 1884885, S2CID 14804110

archive.org

Tchébychef, P. (1860). "Sur le développement des fonctions à une seule variable" [On the development of single-variable functions]. Bulletin de l'Académie impériale des sciences de St.-Pétersbourg (in French). 1: 193–200. Collected in Œuvres I, 501–508.

arxiv.org

Banderier, Cyril; Bousquet-Mélou, Mireille; Denise, Alain; Flajolet, Philippe; Gardy, Danièle; Gouyou-Beauchamps, Dominique (2002), "Generating functions for generating trees", Discrete Mathematics, 246 (1–3): 29–55, arXiv:math/0411250, doi:10.1016/S0012-365X(01)00250-3, MR 1884885, S2CID 14804110

biodiversitylibrary.org

Laplace (1811). "Mémoire sur les intégrales définies et leur application aux probabilités, et spécialement a la recherche du milieu qu'il faut choisir entre les resultats des observations" [Memoire on definite integrals and their application to probabilities, and especially to the search for the mean which must be chosen among the results of observations]. Mémoires de la Classe des Sciences Mathématiques et Physiques de l'Institut Impérial de France (in French). 11: 297–347.
Tchébychef, P. (1860). "Sur le développement des fonctions à une seule variable" [On the development of single-variable functions]. Bulletin de l'Académie impériale des sciences de St.-Pétersbourg (in French). 1: 193–200. Collected in Œuvres I, 501–508.
Hermite, C. (1864). "Sur un nouveau développement en série de fonctions" [On a new development in function series]. C. R. Acad. Sci. Paris (in French). 58: 93–100, 266–273. Collected in Œuvres II, 293–308.

bnf.fr

gallica.bnf.fr

Laplace, P.-S. (1812), Théorie analytique des probabilités [Analytic Probability Theory], vol. 2, pp. 194–203 Collected in Œuvres complètes VII.

brown.edu

cfm.brown.edu

"MATHEMATICA tutorial, part 2.5: Hermite expansion". www.cfm.brown.edu. Retrieved 2023-12-24.

doi.org

Askey, Richard; Wainger, Stephen (1965). "Mean Convergence of Expansions in Laguerre and Hermite Series". American Journal of Mathematics. 87 (3): 695–708. doi:10.2307/2373069. ISSN 0002-9327.
Indritz, Jack (1961), "An inequality for Hermite polynomials", Proceedings of the American Mathematical Society, 12 (6): 981–983, doi:10.1090/S0002-9939-1961-0132852-2, MR 0132852
Groenewold, H. J. (1946). "On the Principles of elementary quantum mechanics". Physica. 12 (7): 405–460. Bibcode:1946Phy....12..405G. doi:10.1016/S0031-8914(46)80059-4.
Banderier, Cyril; Bousquet-Mélou, Mireille; Denise, Alain; Flajolet, Philippe; Gardy, Danièle; Gouyou-Beauchamps, Dominique (2002), "Generating functions for generating trees", Discrete Mathematics, 246 (1–3): 29–55, arXiv:math/0411250, doi:10.1016/S0012-365X(01)00250-3, MR 1884885, S2CID 14804110

harvard.edu

ui.adsabs.harvard.edu

Groenewold, H. J. (1946). "On the Principles of elementary quantum mechanics". Physica. 12 (7): 405–460. Bibcode:1946Phy....12..405G. doi:10.1016/S0031-8914(46)80059-4.

jstor.org

Askey, Richard; Wainger, Stephen (1965). "Mean Convergence of Expansions in Laguerre and Hermite Series". American Journal of Mathematics. 87 (3): 695–708. doi:10.2307/2373069. ISSN 0002-9327.

loc.gov

lccn.loc.gov

Abramowitz & Stegun 1983, p. 508–510, 13.6.38 and 13.5.16. Abramowitz, Milton; Stegun, Irene Ann, eds. (1983) [June 1964]. "Chapter 22". Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Applied Mathematics Series. Vol. 55 (Ninth reprint with additional corrections of tenth original printing with corrections (December 1972); first ed.). Washington D.C.; New York: United States Department of Commerce, National Bureau of Standards; Dover Publications. p. 773. ISBN 978-0-486-61272-0. LCCN 64-60036. MR 0167642. LCCN 65-12253.

loc.gov

Abramowitz & Stegun 1983, p. 508–510, 13.6.38 and 13.5.16. Abramowitz, Milton; Stegun, Irene Ann, eds. (1983) [June 1964]. "Chapter 22". Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Applied Mathematics Series. Vol. 55 (Ninth reprint with additional corrections of tenth original printing with corrections (December 1972); first ed.). Washington D.C.; New York: United States Department of Commerce, National Bureau of Standards; Dover Publications. p. 773. ISBN 978-0-486-61272-0. LCCN 64-60036. MR 0167642. LCCN 65-12253.

nist.gov

dlmf.nist.gov

Tom H. Koornwinder, Roderick S. C. Wong, and Roelof Koekoek et al. (2010) and Abramowitz & Stegun. Koornwinder, Tom H.; Wong, Roderick S. C.; Koekoek, Roelof; Swarttouw, René F. (2010), "Orthogonal Polynomials", in Olver, Frank W. J.; Lozier, Daniel M.; Boisvert, Ronald F.; Clark, Charles W. (eds.), NIST Handbook of Mathematical Functions, Cambridge University Press, ISBN 978-0-521-19225-5, MR 2723248.
"18. Orthogonal Polynomials, Classical Orthogonal Polynomials, Sums". Digital Library of Mathematical Functions. National Institute of Standards and Technology. Retrieved 30 January 2015.

nrbook.com

apps.nrbook.com

Erdélyi et al. 1955, p. 207. Erdélyi, Arthur; Magnus, Wilhelm; Oberhettinger, Fritz; Tricomi, Francesco G. (1955), Higher transcendental functions (PDF), vol. II, McGraw-Hill, ISBN 978-0-07-019546-2
Erdélyi et al. 1955, p. 194, 10.13 (22). Erdélyi, Arthur; Magnus, Wilhelm; Oberhettinger, Fritz; Tricomi, Francesco G. (1955), Higher transcendental functions (PDF), vol. II, McGraw-Hill, ISBN 978-0-07-019546-2

semanticscholar.org

api.semanticscholar.org

Banderier, Cyril; Bousquet-Mélou, Mireille; Denise, Alain; Flajolet, Philippe; Gardy, Danièle; Gouyou-Beauchamps, Dominique (2002), "Generating functions for generating trees", Discrete Mathematics, 246 (1–3): 29–55, arXiv:math/0411250, doi:10.1016/S0012-365X(01)00250-3, MR 1884885, S2CID 14804110

sfu.ca

math.sfu.ca

Abramowitz & Stegun 1983, p. 508–510, 13.6.38 and 13.5.16. Abramowitz, Milton; Stegun, Irene Ann, eds. (1983) [June 1964]. "Chapter 22". Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Applied Mathematics Series. Vol. 55 (Ninth reprint with additional corrections of tenth original printing with corrections (December 1972); first ed.). Washington D.C.; New York: United States Department of Commerce, National Bureau of Standards; Dover Publications. p. 773. ISBN 978-0-486-61272-0. LCCN 64-60036. MR 0167642. LCCN 65-12253.

ubc.ca

math.ubc.ca

Abramowitz & Stegun 1983, p. 508–510, 13.6.38 and 13.5.16. Abramowitz, Milton; Stegun, Irene Ann, eds. (1983) [June 1964]. "Chapter 22". Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Applied Mathematics Series. Vol. 55 (Ninth reprint with additional corrections of tenth original printing with corrections (December 1972); first ed.). Washington D.C.; New York: United States Department of Commerce, National Bureau of Standards; Dover Publications. p. 773. ISBN 978-0-486-61272-0. LCCN 64-60036. MR 0167642. LCCN 65-12253.

uni-goettingen.de

resolver.sub.uni-goettingen.de

Mehler, F. G. (1866), "Ueber die Entwicklung einer Function von beliebig vielen Variabeln nach Laplaceschen Functionen höherer Ordnung" [On the development of a function of arbitrarily many variables according to higher-order Laplace functions], Journal für die Reine und Angewandte Mathematik (in German) (66): 161–176, ISSN 0075-4102, ERAM 066.1720cj. See p. 174, eq. (18) and p. 173, eq. (13).

worldcat.org

Askey, Richard; Wainger, Stephen (1965). "Mean Convergence of Expansions in Laguerre and Hermite Series". American Journal of Mathematics. 87 (3): 695–708. doi:10.2307/2373069. ISSN 0002-9327.
Mehler, F. G. (1866), "Ueber die Entwicklung einer Function von beliebig vielen Variabeln nach Laplaceschen Functionen höherer Ordnung" [On the development of a function of arbitrarily many variables according to higher-order Laplace functions], Journal für die Reine und Angewandte Mathematik (in German) (66): 161–176, ISSN 0075-4102, ERAM 066.1720cj. See p. 174, eq. (18) and p. 173, eq. (13).

zbmath.org

Mehler, F. G. (1866), "Ueber die Entwicklung einer Function von beliebig vielen Variabeln nach Laplaceschen Functionen höherer Ordnung" [On the development of a function of arbitrarily many variables according to higher-order Laplace functions], Journal für die Reine und Angewandte Mathematik (in German) (66): 161–176, ISSN 0075-4102, ERAM 066.1720cj. See p. 174, eq. (18) and p. 173, eq. (13).