Euler's constant (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Euler's constant" in English language version.

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Ramaré, Olivier (2022). Excursions in Multiplicative Number Theory. Birkhäuser Advanced Texts: Basel Textbooks. Basel: Birkhäuser/Springer. p. 131. doi:10.1007/978-3-030-73169-4. ISBN 978-3-030-73168-7. MR 4400952. S2CID 247271545.

ams.org

Brent, Richard P.; McMillan, Edwin M. (1980). "Some new algorithms for high-precision computation of Euler's constant". Mathematics of Computation. 34 (149): 305–312. doi:10.1090/S0025-5718-1980-0551307-4. ISSN 0025-5718.

anu.edu.au (Global: 942^nd place; English: 597^th place)

maths-people.anu.edu.au

Brent, Richard P. (1994). "Ramanujan and Euler's Constant" (PDF). Mathematics of Computation 1943–1993: A Half-Century of Computational Mathematics. Proceedings of Symposia in Applied Mathematics. Vol. 48. pp. 541–545. doi:10.1090/psapm/048/1314887. ISBN 978-0-8218-0291-5.

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

Lagarias 2013. Lagarias, Jeffrey C. (2013). "Euler's constant: Euler's work and modern developments". Bulletin of the American Mathematical Society. 50 (4): 556. arXiv:1303.1856. doi:10.1090/s0273-0979-2013-01423-x. S2CID 119612431.
Caves, Carlton M.; Fuchs, Christopher A. (1996). "Quantum information: How much information in a state vector?". The Dilemma of Einstein, Podolsky and Rosen – 60 Years Later. Israel Physical Society. arXiv:quant-ph/9601025. Bibcode:1996quant.ph..1025C. ISBN 9780750303941. OCLC 36922834.
See also Sondow, Jonathan (2003). "Criteria for irrationality of Euler's constant". Proceedings of the American Mathematical Society. 131 (11): 3335–3344. arXiv:math.NT/0209070. doi:10.1090/S0002-9939-03-07081-3. S2CID 91176597.
Aptekarev, A. I. (28 February 2009). "On linear forms containing the Euler constant". arXiv:0902.1768 [math.NT].
Diamond, H. G.; Ford, K. (2008). "Generalized Euler constants". Mathematical Proceedings of the Cambridge Philosophical Society. 145 (1). Cambridge University Press: 27–41. arXiv:math/0703508. Bibcode:2008MPCPS.145...27D. doi:10.1017/S0305004108001187.
Pilehrood, Khodabakhsh Hessami; Pilehrood, Tatiana Hessami (2013-12-29), On a continued fraction expansion for Euler's constant, arXiv:1010.1420
Wolf, Marek (2019). "6+infinity new expressions for the Euler-Mascheroni constant". arXiv:1904.09855 [math.NT]. The above sum is real and convergent when zeros $\rho$ and complex conjugate ${\bar {\rho }}$ are paired together and summed according to increasing absolute values of the imaginary parts of $\rho$ . See formula 11 on page 3. Note the typographical error in the numerator of Wolf's sum over zeros, which should be 2 rather than 1.
Villarino, Mark B. (2007). "Ramanujan's Harmonic Number Expansion into Negative Powers of a Triangular Number". arXiv:0707.3950 [math.CA]. It would also be interesting to develop an expansion for n! into powers of m, a new Stirling expansion, as it were. See formula 1.8 on page 3.
Lagarias 2013, p. 13. Lagarias, Jeffrey C. (2013). "Euler's constant: Euler's work and modern developments". Bulletin of the American Mathematical Society. 50 (4): 556. arXiv:1303.1856. doi:10.1090/s0273-0979-2013-01423-x. S2CID 119612431.
Sondow, Jonathan; Zudilin, Wadim (2006). "Euler's constant, $q$ -logarithms, and formulas of Ramanujan and Gosper". The Ramanujan Journal. 12 (2): 225–244. arXiv:math.NT/0304021. doi:10.1007/s11139-006-0075-1. S2CID 1368088.
Sondow, Jonathan (2005). "Double integrals for Euler's constant and $\log {\frac {4}{\pi }}$ and an analog of Hadjicostas's formula". American Mathematical Monthly. 112 (1): 61–65. arXiv:math.CA/0211148. doi:10.2307/30037385. JSTOR 30037385.
Sondow, Jonathan (1 August 2005a). New Vacca-type rational series for Euler's constant and its 'alternating' analog $\log {\frac {4}{\pi }}$ . arXiv:math.NT/0508042.
Blagouchine, Iaroslav V. (2016). "Expansions of generalized Euler's constants into the series of polynomials in $π -2$ and into the formal enveloping series with rational coefficients only". J. Number Theory. 158: 365–396. arXiv:1501.00740. doi:10.1016/j.jnt.2015.06.012.
Pilehrood, Khodabakhsh Hessami; Pilehrood, Tatiana Hessami (2008-08-04), Vacca-type series for values of the generalized-Euler-constant function and its derivative, arXiv:0808.0410
Blagouchine, Iaroslav V. (2018). "Three notes on Ser's and Hasse's representations for the zeta-functions". INTEGERS: The Electronic Journal of Combinatorial Number Theory. 18A (#A3): 1–45. arXiv:1606.02044. Bibcode:2016arXiv160602044B. doi:10.5281/zenodo.10581385.
Sondow, Jonathan (2003). "An infinite product for $e γ$ via hypergeometric formulas for Euler's constant, $γ$ ". arXiv:math.CA/0306008.

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

Bretschneider 1837, " $γ = c$ = 0,5772156649015328606181120900823..." on p. 260.
De Morgan, Augustus (1836–1842). The differential and integral calculus. London: Baldwin and Craddoc. " $γ$ " on p. 578.
Finch, Steven R. (2003-08-18). Mathematical Constants. Cambridge University Press. ISBN 978-0-521-81805-6.
Conway, John H.; Guy, Richard (1998-03-16). The Book of Numbers. Springer Science & Business Media. ISBN 978-0-387-97993-9.
Tenenbaum, Gérald (2015-07-16). Introduction to Analytic and Probabilistic Number Theory. American Mathematical Soc. ISBN 978-0-8218-9854-3.
Lodge, A. (1904). "An approximate expression for the value of 1 + 1/2 + 1/3 + ... + 1/r". Messenger of Mathematics. 30: 103–107.
Ramaré, Olivier (2022). Excursions in Multiplicative Number Theory. Birkhäuser Advanced Texts: Basel Textbooks. Basel: Birkhäuser/Springer. p. 131. doi:10.1007/978-3-030-73169-4. ISBN 978-3-030-73168-7. MR 4400952. S2CID 247271545.

carmamaths.org (Global: low place; English: low place)

Mahler, Kurt (4 June 1968). "Applications of a theorem by A. B. Shidlovski" (PDF). Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences. 305 (1481): 149–173. Bibcode:1968RSPSA.305..149M. doi:10.1098/rspa.1968.0111. S2CID 123486171.

colgate.edu (Global: low place; English: 9,382^nd place)

math.colgate.edu

Blagouchine, Iaroslav V. (2018). "Three notes on Ser's and Hasse's representations for the zeta-functions". INTEGERS: The Electronic Journal of Combinatorial Number Theory. 18A (#A3): 1–45. arXiv:1606.02044. Bibcode:2016arXiv160602044B. doi:10.5281/zenodo.10581385.

dbraulibrary.org.in (Global: low place; English: low place)

Bromwich, Thomas John I'Anson (2005) [1908]. An Introduction to the Theory of Infinite Series (PDF) (3rd ed.). United Kingdom: American Mathematical Society. p. 460. See exercise 18.

degruyter.com (Global: 1,425^th place; English: 1,138^th place)

Oettinger, Ludwig (1862-01-01). "Ueber die richtige Werthbestimmung der Constante des Integrallogarithmus". Journal für die reine und angewandte Mathematik (in German). 60: 375–376. doi:10.1515/crll.1862.60.375. ISSN 1435-5345.

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

Lagarias 2013. Lagarias, Jeffrey C. (2013). "Euler's constant: Euler's work and modern developments". Bulletin of the American Mathematical Society. 50 (4): 556. arXiv:1303.1856. doi:10.1090/s0273-0979-2013-01423-x. S2CID 119612431.
Brent, Richard P. (1994). "Ramanujan and Euler's Constant" (PDF). Mathematics of Computation 1943–1993: A Half-Century of Computational Mathematics. Proceedings of Symposia in Applied Mathematics. Vol. 48. pp. 541–545. doi:10.1090/psapm/048/1314887. ISBN 978-0-8218-0291-5.
Davis, P. J. (1959). "Leonhard Euler's Integral: A Historical Profile of the Gamma Function". American Mathematical Monthly. 66 (10): 849–869. doi:10.2307/2309786. JSTOR 2309786. Archived from the original on 7 November 2012. Retrieved 3 December 2016.
Blagouchine, Iaroslav V. (2014-10-01). "Rediscovery of Malmsten's integrals, their evaluation by contour integration methods and some related results". The Ramanujan Journal. 35 (1): 21–110. doi:10.1007/s11139-013-9528-5. ISSN 1572-9303.
Rosser, J. Barkley; Schoenfeld, Lowell (1962). "Approximate formulas for some functions of prime numbers". Illinois Journal of Mathematics. 6 (1): 64–94. doi:10.1215/ijm/1255631807. ISSN 0019-2082.
Pintz, János (1997-04-01). "Very Large Gaps between Consecutive Primes". Journal of Number Theory. 63 (2): 286–301. doi:10.1006/jnth.1997.2081. ISSN 0022-314X.
Connallon, Tim; Hodgins, Kathryn A. (October 2021). "Allen Orr and the genetics of adaptation". Evolution. 75 (11): 2624–2640. doi:10.1111/evo.14372. PMID 34606622. S2CID 238357410.
See also Sondow, Jonathan (2003). "Criteria for irrationality of Euler's constant". Proceedings of the American Mathematical Society. 131 (11): 3335–3344. arXiv:math.NT/0209070. doi:10.1090/S0002-9939-03-07081-3. S2CID 91176597.
Rivoal, Tanguy (2012). "On the arithmetic nature of the values of the gamma function, Euler's constant, and Gompertz's constant". Michigan Mathematical Journal. 61 (2): 239–254. doi:10.1307/mmj/1339011525. ISSN 0026-2285.
Mahler, Kurt (4 June 1968). "Applications of a theorem by A. B. Shidlovski" (PDF). Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences. 305 (1481): 149–173. Bibcode:1968RSPSA.305..149M. doi:10.1098/rspa.1968.0111. S2CID 123486171.
Ram Murty, M.; Saradha, N. (2010). "Euler–Lehmer constants and a conjecture of Erdos". Journal of Number Theory. 130 (12): 2671–2681. doi:10.1016/j.jnt.2010.07.004. ISSN 0022-314X.
Murty, M. Ram; Zaytseva, Anastasia (2013). "Transcendence of Generalized Euler Constants". The American Mathematical Monthly. 120 (1): 48–54. doi:10.4169/amer.math.monthly.120.01.048. ISSN 0002-9890. JSTOR 10.4169/amer.math.monthly.120.01.048. S2CID 20495981.
Diamond, H. G.; Ford, K. (2008). "Generalized Euler constants". Mathematical Proceedings of the Cambridge Philosophical Society. 145 (1). Cambridge University Press: 27–41. arXiv:math/0703508. Bibcode:2008MPCPS.145...27D. doi:10.1017/S0305004108001187.
Haible, Bruno; Papanikolaou, Thomas (1998). "Fast multiprecision evaluation of series of rational numbers". In Buhler, Joe P. (ed.). Algorithmic Number Theory. Lecture Notes in Computer Science. Vol. 1423. Springer. pp. 338–350. doi:10.1007/bfb0054873. ISBN 9783540691136.
Brent, Richard P. (1977). "Computation of the Regular Continued Fraction for Euler's Constant". Mathematics of Computation. 31 (139): 771–777. doi:10.2307/2006010. ISSN 0025-5718. JSTOR 2006010.
Sondow, Jonathan (1998). "An antisymmetric formula for Euler's constant". Mathematics Magazine. 71 (3): 219–220. doi:10.1080/0025570X.1998.11996638. Archived from the original on 2011-06-04. Retrieved 2006-05-29.
Boya, L.J. (2008). "Another relation between π, e, γ and ζ(n)". Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas. 102 (2): 199–202. Bibcode:2008RvMad.102..199B. doi:10.1007/BF03191819. γ/2 in (10) reflects the residual (finite part) of ζ(1)/2, of course. See formulas 1 and 10.
Sondow, Jonathan (2005). "Double Integrals for Euler's Constant and $\textstyle {\frac {4}{\pi }}$ and an Analog of Hadjicostas's Formula". The American Mathematical Monthly. 112 (1): 61–65. doi:10.2307/30037385. JSTOR 30037385. Retrieved 2024-04-27.
Chen, Chao-Ping (2018). "Ramanujan's formula for the harmonic number". Applied Mathematics and Computation. 317: 121–128. doi:10.1016/j.amc.2017.08.053. ISSN 0096-3003. Retrieved 2024-04-27.
Whittaker, E.; Watson, G. (2021) [1902]. A Course of Modern Analysis (5th ed.). pp. 271, 275. doi:10.1017/9781009004091. ISBN 9781316518939. See Examples 12.21 and 12.50 for exercises on the derivation of the integral form $\textstyle \int _{-1}^{0}\ln \Gamma (z+1)\,dz$ of the series $\textstyle \sum _{k=1}^{n}{\frac {\zeta (k)}{110_{k}}}=\ln({\sqrt {2\pi }})$ .
Lagarias 2013, p. 13. Lagarias, Jeffrey C. (2013). "Euler's constant: Euler's work and modern developments". Bulletin of the American Mathematical Society. 50 (4): 556. arXiv:1303.1856. doi:10.1090/s0273-0979-2013-01423-x. S2CID 119612431.
Nelsen, R. B. (1991). "Proof without Words: Sum of Reciprocals of Triangular Numbers". Mathematics Magazine. 64 (3): 167. doi:10.1080/0025570X.1991.11977600.
Sondow, Jonathan; Zudilin, Wadim (2006). "Euler's constant, $q$ -logarithms, and formulas of Ramanujan and Gosper". The Ramanujan Journal. 12 (2): 225–244. arXiv:math.NT/0304021. doi:10.1007/s11139-006-0075-1. S2CID 1368088.
Sondow, Jonathan (2005). "Double integrals for Euler's constant and $\log {\frac {4}{\pi }}$ and an analog of Hadjicostas's formula". American Mathematical Monthly. 112 (1): 61–65. arXiv:math.CA/0211148. doi:10.2307/30037385. JSTOR 30037385.
DeTemple, Duane W. (May 1993). "A Quicker Convergence to Euler's Constant". The American Mathematical Monthly. 100 (5): 468–470. doi:10.2307/2324300. ISSN 0002-9890. JSTOR 2324300.
Vacca, G. (1910). "A new analytical expression for the number π and some historical considerations". Bulletin of the American Mathematical Society. 16: 368–369. doi:10.1090/S0002-9904-1910-01919-4.
Blagouchine, Iaroslav V. (2016). "Expansions of generalized Euler's constants into the series of polynomials in $π -2$ and into the formal enveloping series with rational coefficients only". J. Number Theory. 158: 365–396. arXiv:1501.00740. doi:10.1016/j.jnt.2015.06.012.
Blagouchine, Iaroslav V. (2018). "Three notes on Ser's and Hasse's representations for the zeta-functions". INTEGERS: The Electronic Journal of Combinatorial Number Theory. 18A (#A3): 1–45. arXiv:1606.02044. Bibcode:2016arXiv160602044B. doi:10.5281/zenodo.10581385.
Ramaré, Olivier (2022). Excursions in Multiplicative Number Theory. Birkhäuser Advanced Texts: Basel Textbooks. Basel: Birkhäuser/Springer. p. 131. doi:10.1007/978-3-030-73169-4. ISBN 978-3-030-73168-7. MR 4400952. S2CID 247271545.
Choi, Junesang; Srivastava, H.M. (1 September 2010). "Integral Representations for the Euler–Mascheroni Constant $γ$ ". Integral Transforms and Special Functions. 21 (9): 675–690. doi:10.1080/10652461003593294. ISSN 1065-2469. S2CID 123698377.
Oettinger, Ludwig (1862-01-01). "Ueber die richtige Werthbestimmung der Constante des Integrallogarithmus". Journal für die reine und angewandte Mathematik (in German). 60: 375–376. doi:10.1515/crll.1862.60.375. ISSN 1435-5345.
"I. On the calculation of the numerical value of Euler's constant, which Professor Price, of Oxford, calls E". Proceedings of the Royal Society of London. 15: 429–432. 1867-12-31. doi:10.1098/rspl.1866.0100. ISSN 0370-1662.
Knuth, Donald E. (July 1962). "Euler's Constant to 1271 Places". Mathematics of Computation. 16 (79). American Mathematical Society: 275–281. doi:10.2307/2004048. JSTOR 2004048.
Sweeney, Dura W. (1963). "On the computation of Euler's constant". Mathematics of Computation. 17 (82): 170–178. doi:10.1090/S0025-5718-1963-0160308-X. ISSN 0025-5718. S2CID 120162114.
Beyer, W. A.; Waterman, M. S. (1974). "Error Analysis of a Computation of Euler's Constant". Mathematics of Computation. 28 (126): 599–604. doi:10.2307/2005935. ISSN 0025-5718. JSTOR 2005935.
Brent, Richard P.; McMillan, Edwin M. (1980). "Some new algorithms for high-precision computation of Euler's constant". Mathematics of Computation. 34 (149): 305–312. doi:10.1090/S0025-5718-1980-0551307-4. ISSN 0025-5718.

earthlink.net (Global: 7,693^rd place; English: 5,406^th place)

home.earthlink.net

Sondow, Jonathan (1998). "An antisymmetric formula for Euler's constant". Mathematics Magazine. 71 (3): 219–220. doi:10.1080/0025570X.1998.11996638. Archived from the original on 2011-06-04. Retrieved 2006-05-29.

ehfd.github.io (Global: low place; English: low place)

"Euler-Mascheroni Constant". Polymath Collector. 15 February 2020.

eudml.org (Global: low place; English: low place)

Cesàro, E. (1885). "Sur la série harmonique". Nouvelles annales de mathématiques: Journal des candidats aux écoles polytechnique et normale (in French). 4. Carilian-Goeury et Vor Dalmont: 295–296.

free.fr (Global: 321^st place; English: 724^th place)

numbers.computation.free.fr

Sondow, Jonathan (2004). "The Euler constant: γ". Retrieved 2024-11-01.

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

ui.adsabs.harvard.edu

Caves, Carlton M.; Fuchs, Christopher A. (1996). "Quantum information: How much information in a state vector?". The Dilemma of Einstein, Podolsky and Rosen – 60 Years Later. Israel Physical Society. arXiv:quant-ph/9601025. Bibcode:1996quant.ph..1025C. ISBN 9780750303941. OCLC 36922834.
Mahler, Kurt (4 June 1968). "Applications of a theorem by A. B. Shidlovski" (PDF). Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences. 305 (1481): 149–173. Bibcode:1968RSPSA.305..149M. doi:10.1098/rspa.1968.0111. S2CID 123486171.
Diamond, H. G.; Ford, K. (2008). "Generalized Euler constants". Mathematical Proceedings of the Cambridge Philosophical Society. 145 (1). Cambridge University Press: 27–41. arXiv:math/0703508. Bibcode:2008MPCPS.145...27D. doi:10.1017/S0305004108001187.
Boya, L.J. (2008). "Another relation between π, e, γ and ζ(n)". Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas. 102 (2): 199–202. Bibcode:2008RvMad.102..199B. doi:10.1007/BF03191819. γ/2 in (10) reflects the residual (finite part) of ζ(1)/2, of course. See formulas 1 and 10.
Blagouchine, Iaroslav V. (2018). "Three notes on Ser's and Hasse's representations for the zeta-functions". INTEGERS: The Electronic Journal of Combinatorial Number Theory. 18A (#A3): 1–45. arXiv:1606.02044. Bibcode:2016arXiv160602044B. doi:10.5281/zenodo.10581385.

imj-prg.fr (Global: low place; English: low place)

webusers.imj-prg.fr

Waldschmidt, Michel (2023). "On Euler's Constant" (PDF). Sorbonne Université, Institut de Mathématiques de Jussieu, Paris.
Waldschmidt, Michel (2023). "Some of the most famous open problems in number theory" (PDF).

jstor.org (Global: 26^th place; English: 20^th place)

Davis, P. J. (1959). "Leonhard Euler's Integral: A Historical Profile of the Gamma Function". American Mathematical Monthly. 66 (10): 849–869. doi:10.2307/2309786. JSTOR 2309786. Archived from the original on 7 November 2012. Retrieved 3 December 2016.
Murty, M. Ram; Zaytseva, Anastasia (2013). "Transcendence of Generalized Euler Constants". The American Mathematical Monthly. 120 (1): 48–54. doi:10.4169/amer.math.monthly.120.01.048. ISSN 0002-9890. JSTOR 10.4169/amer.math.monthly.120.01.048. S2CID 20495981.
Brent, Richard P. (1977). "Computation of the Regular Continued Fraction for Euler's Constant". Mathematics of Computation. 31 (139): 771–777. doi:10.2307/2006010. ISSN 0025-5718. JSTOR 2006010.
Sondow, Jonathan (2005). "Double Integrals for Euler's Constant and $\textstyle {\frac {4}{\pi }}$ and an Analog of Hadjicostas's Formula". The American Mathematical Monthly. 112 (1): 61–65. doi:10.2307/30037385. JSTOR 30037385. Retrieved 2024-04-27.
Sondow, Jonathan (2005). "Double integrals for Euler's constant and $\log {\frac {4}{\pi }}$ and an analog of Hadjicostas's formula". American Mathematical Monthly. 112 (1): 61–65. arXiv:math.CA/0211148. doi:10.2307/30037385. JSTOR 30037385.
DeTemple, Duane W. (May 1993). "A Quicker Convergence to Euler's Constant". The American Mathematical Monthly. 100 (5): 468–470. doi:10.2307/2324300. ISSN 0002-9890. JSTOR 2324300.
Knuth, Donald E. (July 1962). "Euler's Constant to 1271 Places". Mathematics of Computation. 16 (79). American Mathematical Society: 275–281. doi:10.2307/2004048. JSTOR 2004048.
Beyer, W. A.; Waterman, M. S. (1974). "Error Analysis of a Computation of Euler's Constant". Mathematics of Computation. 28 (126): 599–604. doi:10.2307/2005935. ISSN 0025-5718. JSTOR 2005935.

lri.fr (Global: low place; English: low place)

Melquiond, Guillaume; Nowak, W. Georg; Zimmermann, Paul. "Numerical approximation of the Masser-Gramain constant to four decimal digits" (PDF). Retrieved 2024-10-03.

maa.org (Global: 3,479^th place; English: 2,444^th place)

mathdl.maa.org

Davis, P. J. (1959). "Leonhard Euler's Integral: A Historical Profile of the Gamma Function". American Mathematical Monthly. 66 (10): 849–869. doi:10.2307/2309786. JSTOR 2309786. Archived from the original on 7 November 2012. Retrieved 3 December 2016.

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

pubmed.ncbi.nlm.nih.gov

Connallon, Tim; Hodgins, Kathryn A. (October 2021). "Allen Orr and the genetics of adaptation". Evolution. 75 (11): 2624–2640. doi:10.1111/evo.14372. PMID 34606622. S2CID 238357410.

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

dlmf.nist.gov

"DLMF: §5.17 Barnes' 𝐺-Function (Double Gamma Function) ‣ Properties ‣ Chapter 5 Gamma Function". dlmf.nist.gov. Retrieved 2024-11-01.
"DLMF: §2.5 Mellin Transform Methods ‣ Areas ‣ Chapter 2 Asymptotic Approximations". dlmf.nist.gov. Retrieved 2024-11-01.
"DLMF: §6.6 Power Series ‣ Properties ‣ Chapter 6 Exponential, Logarithmic, Sine, and Cosine Integrals". dlmf.nist.gov. Retrieved 2024-11-01.
"DLMF: §10.32 Integral Representations ‣ Modified Bessel Functions ‣ Chapter 10 Bessel Functions". dlmf.nist.gov. Retrieved 2024-11-01.
"DLMF: §10.22 Integrals ‣ Bessel and Hankel Functions ‣ Chapter 10 Bessel Functions". dlmf.nist.gov. Retrieved 2024-11-01.
"DLMF: §10.8 Power Series ‣ Bessel Functions and Hankel Functions ‣ Chapter 10 Bessel Functions". dlmf.nist.gov. Retrieved 2024-11-01.
"DLMF: §10.24 Functions of Imaginary Order ‣ Bessel and Hankel Functions ‣ Chapter 10 Bessel Functions". dlmf.nist.gov. Retrieved 2024-11-01.
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