Bessel function (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Bessel function" in English language version.

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22ubc.ca

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2projecteuclid.org

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1uwaterloo.ca

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arxiv.org

Wilensky, Michael; Brown, Jordan; Hazelton, Bryna (June 2023). "Why and when to expect Gaussian error distributions in epoch of reionization 21-cm power spectrum measurements". Monthly Notices of the Royal Astronomical Society. 521 (4): 5191–5206. arXiv:2211.13576. doi:10.1093/mnras/stad863.
Sung, S.; Hovden, R. (2022). "On Infinite Series of Bessel functions of the First Kind". arXiv:2211.01148 [math-ph].

books.google.com

Watson, p. 176
Watson, p. 178.
Watson, p. 181.
Watson, G. N. (25 August 1995). A Treatise on the Theory of Bessel Functions. Cambridge University Press. ISBN 9780521483919. Retrieved 25 March 2018 – via Google Books.

dml.cz

Referred to as such in: Teichroew, D. (1957). "The Mixture of Normal Distributions with Different Variances" (PDF). The Annals of Mathematical Statistics. 28 (2): 510–512. doi:10.1214/aoms/1177706981.

doi.org

Dutka, Jacques (1995). "On the early history of Bessel functions". Archive for History of Exact Sciences. 49 (2): 105–134. doi:10.1007/BF00376544.
Wilensky, Michael; Brown, Jordan; Hazelton, Bryna (June 2023). "Why and when to expect Gaussian error distributions in epoch of reionization 21-cm power spectrum measurements". Monthly Notices of the Royal Astronomical Society. 521 (4): 5191–5206. arXiv:2211.13576. doi:10.1093/mnras/stad863.
Dixon; Ferrar, W.L. (1930). "A direct proof of Nicholson's integral". The Quarterly Journal of Mathematics. Oxford: 236–238. doi:10.1093/qmath/os-1.1.236.
Khokonov, M. Kh. (2004). "Cascade Processes of Energy Loss by Emission of Hard Photons". Journal of Experimental and Theoretical Physics. 99 (4): 690–707. Bibcode:2004JETP...99..690K. doi:10.1134/1.1826160. S2CID 122599440.. Derived from formulas sourced to I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Fizmatgiz, Moscow, 1963; Academic Press, New York, 1980).
Referred to as such in: Teichroew, D. (1957). "The Mixture of Normal Distributions with Different Variances" (PDF). The Annals of Mathematical Statistics. 28 (2): 510–512. doi:10.1214/aoms/1177706981.
Du, Hong (2004). "Mie-scattering calculation". Applied Optics. 43 (9): 1951–1956. Bibcode:2004ApOpt..43.1951D. doi:10.1364/ao.43.001951. PMID 15065726.
Siegel, Carl L. (2014). "Über einige Anwendungen diophantischer Approximationen". On Some Applications of Diophantine Approximations: a translation of Carl Ludwig Siegel's Über einige Anwendungen diophantischer Approximationen by Clemens Fuchs, with a commentary and the article Integral points on curves: Siegel's theorem after Siegel's proof by Clemens Fuchs and Umberto Zannier (in German). Scuola Normale Superiore. pp. 81–138. doi:10.1007/978-88-7642-520-2_2. ISBN 978-88-7642-520-2.
James, R. D. (November 1950). "Review: Carl Ludwig Siegel, Transcendental numbers". Bulletin of the American Mathematical Society. 56 (6): 523–526. doi:10.1090/S0002-9904-1950-09435-X.
Truesdell, C. (1950). "On the Addition and Multiplication Theorems for the Special Functions". Proceedings of the National Academy of Sciences. 1950 (12): 752–757. Bibcode:1950PNAS...36..752T. doi:10.1073/pnas.36.12.752. PMC 1063284. PMID 16578355.
Lorch, Lee; Muldoon, Martin E. (1995). "Transcendentality of zeros of higher dereivatives of functions involving Bessel functions". International Journal of Mathematics and Mathematical Sciences. 18 (3): 551–560. doi:10.1155/S0161171295000706.

ghostarchive.org

"Bessel Functions of the First and Second Kind" (PDF). mhtlab.uwaterloo.ca. p. 3. Archived (PDF) from the original on 2022-10-09. Retrieved 24 May 2022.

harvard.edu

ui.adsabs.harvard.edu

Khokonov, M. Kh. (2004). "Cascade Processes of Energy Loss by Emission of Hard Photons". Journal of Experimental and Theoretical Physics. 99 (4): 690–707. Bibcode:2004JETP...99..690K. doi:10.1134/1.1826160. S2CID 122599440.. Derived from formulas sourced to I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Fizmatgiz, Moscow, 1963; Academic Press, New York, 1980).
Du, Hong (2004). "Mie-scattering calculation". Applied Optics. 43 (9): 1951–1956. Bibcode:2004ApOpt..43.1951D. doi:10.1364/ao.43.001951. PMID 15065726.
Truesdell, C. (1950). "On the Addition and Multiplication Theorems for the Special Functions". Proceedings of the National Academy of Sciences. 1950 (12): 752–757. Bibcode:1950PNAS...36..752T. doi:10.1073/pnas.36.12.752. PMC 1063284. PMID 16578355.

loc.gov

lccn.loc.gov

Gradshteyn, Izrail Solomonovich; Ryzhik, Iosif Moiseevich; Geronimus, Yuri Veniaminovich; Tseytlin, Michail Yulyevich; Jeffrey, Alan (2015) [October 2014]. "8.411.10.". In Zwillinger, Daniel; Moll, Victor Hugo (eds.). Table of Integrals, Series, and Products. Translated by Scripta Technica, Inc. (8 ed.). Academic Press, Inc. ISBN 978-0-12-384933-5. LCCN 2014010276.

nbi.dk

"Integral representations of the Bessel function". www.nbi.dk. Archived from the original on 3 October 2022. Retrieved 25 March 2018.

nih.gov

pubmed.ncbi.nlm.nih.gov

Du, Hong (2004). "Mie-scattering calculation". Applied Optics. 43 (9): 1951–1956. Bibcode:2004ApOpt..43.1951D. doi:10.1364/ao.43.001951. PMID 15065726.
Truesdell, C. (1950). "On the Addition and Multiplication Theorems for the Special Functions". Proceedings of the National Academy of Sciences. 1950 (12): 752–757. Bibcode:1950PNAS...36..752T. doi:10.1073/pnas.36.12.752. PMC 1063284. PMID 16578355.

ncbi.nlm.nih.gov

Truesdell, C. (1950). "On the Addition and Multiplication Theorems for the Special Functions". Proceedings of the National Academy of Sciences. 1950 (12): 752–757. Bibcode:1950PNAS...36..752T. doi:10.1073/pnas.36.12.752. PMC 1063284. PMID 16578355.

nist.gov

dlmf.nist.gov

NIST Digital Library of Mathematical Functions, (10.8.1). Accessed on line Oct. 25, 2016.
"Modified Bessel Functions §10.32 Integral Representations". NIST Digital Library of Mathematical Functions. NIST. Retrieved 2024-11-20.
NIST Digital Library of Mathematical Functions, Section 10.11.

ohio-state.edu

math.ohio-state.edu

"Properties of Hankel and Bessel Functions". Archived from the original on 2010-09-23. Retrieved 2010-10-18.

projecteuclid.org

Fröhlich and Spencer 1981 Appendix B
James, R. D. (November 1950). "Review: Carl Ludwig Siegel, Transcendental numbers". Bulletin of the American Mathematical Society. 56 (6): 523–526. doi:10.1090/S0002-9904-1950-09435-X.

sciencedirect.com

L.V. Babushkina, M.K. Kerimov, A.I. Nikitin, Algorithms for computing Bessel functions of half-integer order with complex arguments, p. 110, p. 111.

semanticscholar.org

api.semanticscholar.org

Khokonov, M. Kh. (2004). "Cascade Processes of Energy Loss by Emission of Hard Photons". Journal of Experimental and Theoretical Physics. 99 (4): 690–707. Bibcode:2004JETP...99..690K. doi:10.1134/1.1826160. S2CID 122599440.. Derived from formulas sourced to I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Fizmatgiz, Moscow, 1963; Academic Press, New York, 1980).

springer.com

link.springer.com

Siegel, Carl L. (2014). "Über einige Anwendungen diophantischer Approximationen". On Some Applications of Diophantine Approximations: a translation of Carl Ludwig Siegel's Über einige Anwendungen diophantischer Approximationen by Clemens Fuchs, with a commentary and the article Integral points on curves: Siegel's theorem after Siegel's proof by Clemens Fuchs and Umberto Zannier (in German). Scuola Normale Superiore. pp. 81–138. doi:10.1007/978-88-7642-520-2_2. ISBN 978-88-7642-520-2.

ubc.ca

personal.math.ubc.ca

Abramowitz and Stegun, p. 360, 9.1.10.
Abramowitz and Stegun, p. 358, 9.1.5.
Abramowitz and Stegun, p. 362, 9.1.69.
Abramowitz and Stegun, p. 358, 9.1.3, 9.1.4.
Abramowitz and Stegun, p. 358, 9.1.6.
Abramowitz and Stegun, p. 360, 9.1.25.
Abramowitz and Stegun, p. 375, 9.6.2, 9.6.10, 9.6.11.
Abramowitz and Stegun, p. 375, 9.6.3, 9.6.5.
Abramowitz and Stegun, p. 374, 9.6.1.
Abramowitz and Stegun, p. 437, 10.1.1.
Abramowitz and Stegun, p. 439, 10.1.25, 10.1.26.
Abramowitz and Stegun, p. 438, 10.1.11.
Abramowitz and Stegun, p. 438, 10.1.12.
Abramowitz and Stegun, p. 439, 10.1.39.
Abramowitz and Stegun, p. 439, 10.1.23, 10.1.24.
Abramowitz and Stegun, p. 364, 9.2.1.
Abramowitz and Stegun, p. 377, 9.7.1.
Abramowitz and Stegun, p. 378, 9.7.2.
Abramowitz and Stegun, p. 363, 9.1.82 ff.
Abramowitz and Stegun, p. 361, 9.1.27.
Abramowitz and Stegun, p. 361, 9.1.30.
Abramowitz and Stegun, p. 363, 9.1.74.

uwaterloo.ca

mhtlab.uwaterloo.ca

"Bessel Functions of the First and Second Kind" (PDF). mhtlab.uwaterloo.ca. p. 3. Archived (PDF) from the original on 2022-10-09. Retrieved 24 May 2022.

web.archive.org

"Properties of Hankel and Bessel Functions". Archived from the original on 2010-09-23. Retrieved 2010-10-18.
"Integral representations of the Bessel function". www.nbi.dk. Archived from the original on 3 October 2022. Retrieved 25 March 2018.