Bessel function (English Wikipedia)

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

refsWebsite

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22ubc.ca

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10doi.org

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4books.google.com

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3wolfram.com

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3nist.gov

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3harvard.edu

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3nih.gov

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2arxiv.org

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2web.archive.org

1^st place

2projecteuclid.org

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1ohio-state.edu

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1nbi.dk

low place

1uwaterloo.ca

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1ghostarchive.org

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1semanticscholar.org

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1dml.cz

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1sciencedirect.com

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1loc.gov

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1springer.com

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arxiv.org (Global: 69^th place; English: 59^th place)

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 (Global: 3^rd place; English: 3^rd place)

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 (Global: low place; English: low place)

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 (Global: 2^nd place; English: 2^nd place)

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 (Global: 32^nd place; English: 21^st place)

"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 (Global: 18^th place; English: 17^th place)

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 (Global: 70^th place; English: 63^rd place)

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 (Global: low place; English: low place)

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

nih.gov (Global: 4^th place; English: 4^th place)

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 (Global: 355^th place; English: 454^th place)

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 (Global: 5,528^th place; English: 4,582^nd place)

math.ohio-state.edu

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

projecteuclid.org (Global: 3,707^th place; English: 2,409^th place)

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 (Global: 149^th place; English: 178^th place)

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 (Global: 11^th place; English: 8^th place)

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 (Global: 274^th place; English: 309^th place)

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 (Global: 1,997^th place; English: 1,295^th place)

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 (Global: 3,153^rd place; English: 2,332^nd place)

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 (Global: 1^st place; English: 1^st place)

"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.

Bessel function (English Wikipedia)

arxiv.org (Global: 69^th place; English: 59^th place)

books.google.com (Global: 3^rd place; English: 3^rd place)

dml.cz (Global: low place; English: low place)

doi.org (Global: 2^nd place; English: 2^nd place)

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harvard.edu (Global: 18^th place; English: 17^th place)

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loc.gov (Global: 70^th place; English: 63^rd place)

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nbi.dk (Global: low place; English: low place)

nih.gov (Global: 4^th place; English: 4^th place)

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ncbi.nlm.nih.gov

nist.gov (Global: 355^th place; English: 454^th place)

dlmf.nist.gov

ohio-state.edu (Global: 5,528^th place; English: 4,582^nd place)

math.ohio-state.edu

projecteuclid.org (Global: 3,707^th place; English: 2,409^th place)

sciencedirect.com (Global: 149^th place; English: 178^th place)

semanticscholar.org (Global: 11^th place; English: 8^th place)

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springer.com (Global: 274^th place; English: 309^th place)

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ubc.ca (Global: 1,997^th place; English: 1,295^th place)

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mhtlab.uwaterloo.ca

web.archive.org (Global: 1^st place; English: 1^st place)

wolfram.com (Global: 513^th place; English: 537^th place)

mathworld.wolfram.com

Bessel function (English Wikipedia)

arxiv.org (Global: 69th place; English: 59th place)

books.google.com (Global: 3rd place; English: 3rd place)

dml.cz (Global: low place; English: low place)

doi.org (Global: 2nd place; English: 2nd place)

ghostarchive.org (Global: 32nd place; English: 21st place)

harvard.edu (Global: 18th place; English: 17th place)

ui.adsabs.harvard.edu

loc.gov (Global: 70th place; English: 63rd place)

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nbi.dk (Global: low place; English: low place)

nih.gov (Global: 4th place; English: 4th place)

pubmed.ncbi.nlm.nih.gov

ncbi.nlm.nih.gov

nist.gov (Global: 355th place; English: 454th place)

dlmf.nist.gov

ohio-state.edu (Global: 5,528th place; English: 4,582nd place)

math.ohio-state.edu

projecteuclid.org (Global: 3,707th place; English: 2,409th place)

sciencedirect.com (Global: 149th place; English: 178th place)

semanticscholar.org (Global: 11th place; English: 8th place)

api.semanticscholar.org

springer.com (Global: 274th place; English: 309th place)

link.springer.com

ubc.ca (Global: 1,997th place; English: 1,295th place)

personal.math.ubc.ca

uwaterloo.ca (Global: 3,153rd place; English: 2,332nd place)

mhtlab.uwaterloo.ca

web.archive.org (Global: 1st place; English: 1st place)

wolfram.com (Global: 513th place; English: 537th place)

mathworld.wolfram.com

arxiv.org (Global: 69^th place; English: 59^th place)

books.google.com (Global: 3^rd place; English: 3^rd place)

doi.org (Global: 2^nd place; English: 2^nd place)

ghostarchive.org (Global: 32^nd place; English: 21^st place)

harvard.edu (Global: 18^th place; English: 17^th place)

loc.gov (Global: 70^th place; English: 63^rd place)

nih.gov (Global: 4^th place; English: 4^th place)

nist.gov (Global: 355^th place; English: 454^th place)

ohio-state.edu (Global: 5,528^th place; English: 4,582^nd place)

projecteuclid.org (Global: 3,707^th place; English: 2,409^th place)

sciencedirect.com (Global: 149^th place; English: 178^th place)

semanticscholar.org (Global: 11^th place; English: 8^th place)

springer.com (Global: 274^th place; English: 309^th place)

ubc.ca (Global: 1,997^th place; English: 1,295^th place)

uwaterloo.ca (Global: 3,153^rd place; English: 2,332^nd place)

web.archive.org (Global: 1^st place; English: 1^st place)

wolfram.com (Global: 513^th place; English: 537^th place)