Error function (English Wikipedia)

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

Last modified: 05:48:37, 20 August 2026 (UTC)

Ref.Un. Ref.Website

Global rank English rank

1816doi.org

2^nd place

97semanticscholar.org

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8^th place

77adsabs.harvard.edu

14^th place

9^th place

55arxiv.org

49^th place

31^st place

42psu.edu

299^th place

159^th place

33books.google.com

3^rd place

33archive.org

6^th place

31wisc.edu

891^st place

533^rd place

22wolfram.com

1,091^st place

1,169^th place

22web.archive.org

1^st place

11mathematica-journal.com

low place

11unibo.it

3,746^th place

5,990^th place

11zenodo.org

737^th place

426^th place

11auth.gr

6,694^th place

low place

11escholarship.org

1,477^th place

863^rd place

11academia.edu

105^th place

99^th place

11ssrn.com

907^th place

529^th place

11worldcat.org

4^th place

11stanford.edu

194^th place

182^nd place

11opengroup.org

6,630^th place

5,295^th place

11gnu.org

1,901^st place

1,743^rd place

academia.edu (Global: 105^th place; English: 99^th place)

Winitzki, Sergei (6 February 2008). "A handy approximation for the error function and its inverse".

adsabs.harvard.edu (Global: 14^th place; English: 9^th place)

ui.adsabs.harvard.edu

Chiani, M.; Dardari, D.; Simon, M.K. (2003). "New Exponential Bounds and Approximations for the Computation of Error Probability in Fading Channels" (PDF). IEEE Transactions on Wireless Communications. 2 (4): 840–845. Bibcode:2003ITWC....2..840C. CiteSeerX 10.1.1.190.6761. doi:10.1109/TWC.2003.814350. Archived from the original (PDF) on 20 October 2014. Retrieved 20 October 2014. {{cite journal}}: Cite uses deprecated parameter |citeseerx= (help)
Tanash, I.M.; Riihonen, T. (2020). "Global minimax approximations and bounds for the Gaussian Q-function by sums of exponentials". IEEE Transactions on Communications. 68 (10): 6514–6524. arXiv:2007.06939. Bibcode:2020ITCom..68.6514T. doi:10.1109/TCOMM.2020.3006902. S2CID 220514754.
Tanash, I.M.; Riihonen, T. (2021). "Improved coefficients for the Karagiannidis–Lioumpas approximations and bounds to the Gaussian Q-function". IEEE Communications Letters. 25 (5): 1468–1471. arXiv:2101.07631. Bibcode:2021IComL..25.1468T. doi:10.1109/LCOMM.2021.3052257. S2CID 231639206.
Chang, Seok-Ho; Cosman, Pamela C.; Milstein, Laurence B. (November 2011). "Chernoff-Type Bounds for the Gaussian Error Function". IEEE Transactions on Communications. 59 (11): 2939–2944. Bibcode:2011ITCom..59.2939C. doi:10.1109/TCOMM.2011.072011.100049. S2CID 13636638.
Abreu, Giuseppe (2012). "Very Simple Tight Bounds on the Q-Function". IEEE Transactions on Communications. 60 (9): 2415–2420. Bibcode:2012ITCom..60.2415A. doi:10.1109/TCOMM.2012.080612.110075.
Zaghloul, M. R. (1 March 2007), "On the calculation of the Voigt line profile: a single proper integral with a damped sine integrand", Monthly Notices of the Royal Astronomical Society, 375 (3): 1043–1048, Bibcode:2007MNRAS.375.1043Z, doi:10.1111/j.1365-2966.2006.11377.x
Behnad, Aydin (2020). "A Novel Extension to Craig's Q-Function Formula and Its Application in Dual-Branch EGC Performance Analysis". IEEE Transactions on Communications. 68 (7): 4117–4125. Bibcode:2020ITCom..68.4117B. doi:10.1109/TCOMM.2020.2986209. S2CID 216500014.

archive.org (Global: 6^th place; English: 6^th place)

Schlömilch, Oskar Xavier (1859). "Ueber facultätenreihen". Zeitschrift für Mathematik und Physik (in German). 4: 390–415.
Nielson (1906), p. 283, eq. 3. Nielson, Niels (1906). Handbuch der Theorie der Gammafunktion (in German). Leipzig: Teubner. ISBN 978-1-11464695-7. {{cite book}}: ISBN / Date incompatibility (help)
Winitzki, Sergei (2003). "Uniform approximations for transcendental functions". Computational Science and Its Applications – ICCSA 2003. Lecture Notes in Computer Science. Vol. 2667. Springer, Berlin. pp. 780–789. doi:10.1007/3-540-44839-X_82. ISBN 978-3-540-40155-1.

arxiv.org (Global: 49^th place; English: 31^st place)

Dominici, Diego (2006). "Asymptotic analysis of the derivatives of the inverse error function". arXiv:math/0607230.
Bergsma, Wicher (2006). "On a new correlation coefficient, its orthogonal decomposition and associated tests of independence". arXiv:math/0604627.
Tanash, I.M.; Riihonen, T. (2020). "Global minimax approximations and bounds for the Gaussian Q-function by sums of exponentials". IEEE Transactions on Communications. 68 (10): 6514–6524. arXiv:2007.06939. Bibcode:2020ITCom..68.6514T. doi:10.1109/TCOMM.2020.3006902. S2CID 220514754.
Tanash, I.M.; Riihonen, T. (2021). "Improved coefficients for the Karagiannidis–Lioumpas approximations and bounds to the Gaussian Q-function". IEEE Communications Letters. 25 (5): 1468–1471. arXiv:2101.07631. Bibcode:2021IComL..25.1468T. doi:10.1109/LCOMM.2021.3052257. S2CID 231639206.
Zeng, Caibin; Chen, Yang Cuan (2015). "Global Padé approximations of the generalized Mittag-Leffler function and its inverse". Fractional Calculus and Applied Analysis. 18 (6): 1492–1506. arXiv:1310.5592. doi:10.1515/fca-2015-0086. S2CID 118148950. Indeed, Winitzki [32] provided the so-called global Padé approximation

auth.gr (Global: 6,694^th place; English: low place)

users.auth.gr

Karagiannidis, G. K.; Lioumpas, A. S. (2007). "An improved approximation for the Gaussian Q-function" (PDF). IEEE Communications Letters. 11 (8): 644–646. doi:10.1109/LCOMM.2007.070470. S2CID 4043576.

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

Andrews (1998), p. 110. Andrews, Larry C. (1998) [1992]. Special Functions of Mathematics for Engineers (2nd ed.). Oxford University Press. ISBN 978-0-81942616-1.
Glaisher (1871a). Glaisher, J. W. L. (1871a). "On a class of definite integrals". London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 42 (280): 294–302. doi:10.1080/14786447108640568.
Glaisher (1871b). Glaisher, J. W. L. (1871b). "On a class of definite integrals.—Part II". London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 42 (282): 421–436. doi:10.1080/14786447108640600.

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

Glaisher (1871a). Glaisher, J. W. L. (1871a). "On a class of definite integrals". London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 42 (280): 294–302. doi:10.1080/14786447108640568.
Glaisher (1871b). Glaisher, J. W. L. (1871b). "On a class of definite integrals.—Part II". London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 42 (282): 421–436. doi:10.1080/14786447108640600.
Schöpf & Supancic (2014). Schöpf, H. M.; Supancic, P. H. (2014). "On Bürmann's theorem and its application to problems of linear and nonlinear heat transfer and diffusion". The Mathematica Journal. 16. doi:10.3888/tmj.16-11.
Chiani, M.; Dardari, D.; Simon, M.K. (2003). "New Exponential Bounds and Approximations for the Computation of Error Probability in Fading Channels" (PDF). IEEE Transactions on Wireless Communications. 2 (4): 840–845. Bibcode:2003ITWC....2..840C. CiteSeerX 10.1.1.190.6761. doi:10.1109/TWC.2003.814350. Archived from the original (PDF) on 20 October 2014. Retrieved 20 October 2014. {{cite journal}}: Cite uses deprecated parameter |citeseerx= (help)
Tanash, I.M.; Riihonen, T. (2020). "Global minimax approximations and bounds for the Gaussian Q-function by sums of exponentials". IEEE Transactions on Communications. 68 (10): 6514–6524. arXiv:2007.06939. Bibcode:2020ITCom..68.6514T. doi:10.1109/TCOMM.2020.3006902. S2CID 220514754.
Tanash, I.M.; Riihonen, T. (2020). "Coefficients for Global Minimax Approximations and Bounds for the Gaussian Q-Function by Sums of Exponentials [Data set]". Zenodo. doi:10.5281/zenodo.4112978.
Karagiannidis, G. K.; Lioumpas, A. S. (2007). "An improved approximation for the Gaussian Q-function" (PDF). IEEE Communications Letters. 11 (8): 644–646. doi:10.1109/LCOMM.2007.070470. S2CID 4043576.
Tanash, I.M.; Riihonen, T. (2021). "Improved coefficients for the Karagiannidis–Lioumpas approximations and bounds to the Gaussian Q-function". IEEE Communications Letters. 25 (5): 1468–1471. arXiv:2101.07631. Bibcode:2021IComL..25.1468T. doi:10.1109/LCOMM.2021.3052257. S2CID 231639206.
Chang, Seok-Ho; Cosman, Pamela C.; Milstein, Laurence B. (November 2011). "Chernoff-Type Bounds for the Gaussian Error Function". IEEE Transactions on Communications. 59 (11): 2939–2944. Bibcode:2011ITCom..59.2939C. doi:10.1109/TCOMM.2011.072011.100049. S2CID 13636638.
Winitzki, Sergei (2003). "Uniform approximations for transcendental functions". Computational Science and Its Applications – ICCSA 2003. Lecture Notes in Computer Science. Vol. 2667. Springer, Berlin. pp. 780–789. doi:10.1007/3-540-44839-X_82. ISBN 978-3-540-40155-1.
Zeng, Caibin; Chen, Yang Cuan (2015). "Global Padé approximations of the generalized Mittag-Leffler function and its inverse". Fractional Calculus and Applied Analysis. 18 (6): 1492–1506. arXiv:1310.5592. doi:10.1515/fca-2015-0086. S2CID 118148950. Indeed, Winitzki [32] provided the so-called global Padé approximation
Dia, Yaya D. (2023). "Approximate Incomplete Integrals, Application to Complementary Error Function". SSRN Electronic Journal. doi:10.2139/ssrn.4487559. ISSN 1556-5068.
Abreu, Giuseppe (2012). "Very Simple Tight Bounds on the Q-Function". IEEE Transactions on Communications. 60 (9): 2415–2420. Bibcode:2012ITCom..60.2415A. doi:10.1109/TCOMM.2012.080612.110075.
Cody, W. J. (March 1993), "Algorithm 715: SPECFUN—A portable FORTRAN package of special function routines and test drivers" (PDF), ACM Trans. Math. Softw., 19 (1): 22–32, CiteSeerX 10.1.1.643.4394, doi:10.1145/151271.151273, S2CID 5621105 {{citation}}: Cite uses deprecated parameter |citeseerx= (help)
Zaghloul, M. R. (1 March 2007), "On the calculation of the Voigt line profile: a single proper integral with a damped sine integrand", Monthly Notices of the Royal Astronomical Society, 375 (3): 1043–1048, Bibcode:2007MNRAS.375.1043Z, doi:10.1111/j.1365-2966.2006.11377.x
Behnad, Aydin (2020). "A Novel Extension to Craig's Q-Function Formula and Its Application in Dual-Branch EGC Performance Analysis". IEEE Transactions on Communications. 68 (7): 4117–4125. Bibcode:2020ITCom..68.4117B. doi:10.1109/TCOMM.2020.2986209. S2CID 216500014.

escholarship.org (Global: 1,477^th place; English: 863^rd place)

Chang, Seok-Ho; Cosman, Pamela C.; Milstein, Laurence B. (November 2011). "Chernoff-Type Bounds for the Gaussian Error Function". IEEE Transactions on Communications. 59 (11): 2939–2944. Bibcode:2011ITCom..59.2939C. doi:10.1109/TCOMM.2011.072011.100049. S2CID 13636638.

gnu.org (Global: 1,901^st place; English: 1,743^rd place)

"Special Functions – GSL 2.7 documentation".

mathematica-journal.com (Global: low place; English: low place)

Schöpf & Supancic (2014). Schöpf, H. M.; Supancic, P. H. (2014). "On Bürmann's theorem and its application to problems of linear and nonlinear heat transfer and diffusion". The Mathematica Journal. 16. doi:10.3888/tmj.16-11.

opengroup.org (Global: 6,630^th place; English: 5,295^th place)

pubs.opengroup.org

"math.h - mathematical declarations". opengroup.org. 2018. Retrieved 21 April 2023.

psu.edu (Global: 299^th place; English: 159^th place)

citeseerx.ist.psu.edu

Chiani, M.; Dardari, D.; Simon, M.K. (2003). "New Exponential Bounds and Approximations for the Computation of Error Probability in Fading Channels" (PDF). IEEE Transactions on Wireless Communications. 2 (4): 840–845. Bibcode:2003ITWC....2..840C. CiteSeerX 10.1.1.190.6761. doi:10.1109/TWC.2003.814350. Archived from the original (PDF) on 20 October 2014. Retrieved 20 October 2014. {{cite journal}}: Cite uses deprecated parameter |citeseerx= (help)
Cody, W. J. (March 1993), "Algorithm 715: SPECFUN—A portable FORTRAN package of special function routines and test drivers" (PDF), ACM Trans. Math. Softw., 19 (1): 22–32, CiteSeerX 10.1.1.643.4394, doi:10.1145/151271.151273, S2CID 5621105 {{citation}}: Cite uses deprecated parameter |citeseerx= (help)

semanticscholar.org (Global: 15^th place; English: 8^th place)

api.semanticscholar.org

Tanash, I.M.; Riihonen, T. (2020). "Global minimax approximations and bounds for the Gaussian Q-function by sums of exponentials". IEEE Transactions on Communications. 68 (10): 6514–6524. arXiv:2007.06939. Bibcode:2020ITCom..68.6514T. doi:10.1109/TCOMM.2020.3006902. S2CID 220514754.
Karagiannidis, G. K.; Lioumpas, A. S. (2007). "An improved approximation for the Gaussian Q-function" (PDF). IEEE Communications Letters. 11 (8): 644–646. doi:10.1109/LCOMM.2007.070470. S2CID 4043576.
Tanash, I.M.; Riihonen, T. (2021). "Improved coefficients for the Karagiannidis–Lioumpas approximations and bounds to the Gaussian Q-function". IEEE Communications Letters. 25 (5): 1468–1471. arXiv:2101.07631. Bibcode:2021IComL..25.1468T. doi:10.1109/LCOMM.2021.3052257. S2CID 231639206.
Chang, Seok-Ho; Cosman, Pamela C.; Milstein, Laurence B. (November 2011). "Chernoff-Type Bounds for the Gaussian Error Function". IEEE Transactions on Communications. 59 (11): 2939–2944. Bibcode:2011ITCom..59.2939C. doi:10.1109/TCOMM.2011.072011.100049. S2CID 13636638.
Zeng, Caibin; Chen, Yang Cuan (2015). "Global Padé approximations of the generalized Mittag-Leffler function and its inverse". Fractional Calculus and Applied Analysis. 18 (6): 1492–1506. arXiv:1310.5592. doi:10.1515/fca-2015-0086. S2CID 118148950. Indeed, Winitzki [32] provided the so-called global Padé approximation
Cody, W. J. (March 1993), "Algorithm 715: SPECFUN—A portable FORTRAN package of special function routines and test drivers" (PDF), ACM Trans. Math. Softw., 19 (1): 22–32, CiteSeerX 10.1.1.643.4394, doi:10.1145/151271.151273, S2CID 5621105 {{citation}}: Cite uses deprecated parameter |citeseerx= (help)
Behnad, Aydin (2020). "A Novel Extension to Craig's Q-Function Formula and Its Application in Dual-Branch EGC Performance Analysis". IEEE Transactions on Communications. 68 (7): 4117–4125. Bibcode:2020ITCom..68.4117B. doi:10.1109/TCOMM.2020.2986209. S2CID 216500014.

ssrn.com (Global: 907^th place; English: 529^th place)

Dia, Yaya D. (2023). "Approximate Incomplete Integrals, Application to Complementary Error Function". SSRN Electronic Journal. doi:10.2139/ssrn.4487559. ISSN 1556-5068.

stanford.edu (Global: 194^th place; English: 182^nd place)

wsl.stanford.edu

John W. Craig, A new, simple and exact result for calculating the probability of error for two-dimensional signal constellations Archived 3 April 2012 at the Wayback Machine, Proceedings of the 1991 IEEE Military Communication Conference, vol. 2, pp. 571–575.

unibo.it (Global: 3,746^th place; English: 5,990^th place)

campus.unibo.it

Chiani, M.; Dardari, D.; Simon, M.K. (2003). "New Exponential Bounds and Approximations for the Computation of Error Probability in Fading Channels" (PDF). IEEE Transactions on Wireless Communications. 2 (4): 840–845. Bibcode:2003ITWC....2..840C. CiteSeerX 10.1.1.190.6761. doi:10.1109/TWC.2003.814350. Archived from the original (PDF) on 20 October 2014. Retrieved 20 October 2014. {{cite journal}}: Cite uses deprecated parameter |citeseerx= (help)

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

Chiani, M.; Dardari, D.; Simon, M.K. (2003). "New Exponential Bounds and Approximations for the Computation of Error Probability in Fading Channels" (PDF). IEEE Transactions on Wireless Communications. 2 (4): 840–845. Bibcode:2003ITWC....2..840C. CiteSeerX 10.1.1.190.6761. doi:10.1109/TWC.2003.814350. Archived from the original (PDF) on 20 October 2014. Retrieved 20 October 2014. {{cite journal}}: Cite uses deprecated parameter |citeseerx= (help)
John W. Craig, A new, simple and exact result for calculating the probability of error for two-dimensional signal constellations Archived 3 April 2012 at the Wayback Machine, Proceedings of the 1991 IEEE Military Communication Conference, vol. 2, pp. 571–575.

wisc.edu (Global: 891^st place; English: 533^rd place)

stat.wisc.edu

Cody, W. J. (March 1993), "Algorithm 715: SPECFUN—A portable FORTRAN package of special function routines and test drivers" (PDF), ACM Trans. Math. Softw., 19 (1): 22–32, CiteSeerX 10.1.1.643.4394, doi:10.1145/151271.151273, S2CID 5621105 {{citation}}: Cite uses deprecated parameter |citeseerx= (help)

wolfram.com (Global: 1,091^st place; English: 1,169^th place)

mathworld.wolfram.com

worldcat.org (Global: 4^th place; English: 4^th place)

search.worldcat.org

Dia, Yaya D. (2023). "Approximate Incomplete Integrals, Application to Complementary Error Function". SSRN Electronic Journal. doi:10.2139/ssrn.4487559. ISSN 1556-5068.

zenodo.org (Global: 737^th place; English: 426^th place)

Tanash, I.M.; Riihonen, T. (2020). "Coefficients for Global Minimax Approximations and Bounds for the Gaussian Q-Function by Sums of Exponentials [Data set]". Zenodo. doi:10.5281/zenodo.4112978.

Error function (English Wikipedia)

academia.edu (Global: 105th place; English: 99th place)

adsabs.harvard.edu (Global: 14th place; English: 9th place)

ui.adsabs.harvard.edu

archive.org (Global: 6th place; English: 6th place)

arxiv.org (Global: 49th place; English: 31st place)

auth.gr (Global: 6,694th place; English: low place)

users.auth.gr

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

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

escholarship.org (Global: 1,477th place; English: 863rd place)

gnu.org (Global: 1,901st place; English: 1,743rd place)