Error function (English Wikipedia)

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

refsWebsite

Global rank English rank

16doi.org

2^nd place

7harvard.edu

18^th place

17^th place

7semanticscholar.org

11^th place

8^th place

5arxiv.org

69^th place

59^th place

3books.google.com

3^rd place

3archive.org

6^th place

2wolfram.com

513^th place

537^th place

2psu.edu

207^th place

136^th place

1mathematica-journal.com

low place

1wikipedia.org

low place

1unibo.it

4,963^rd place

7,139^th place

1zenodo.org

621^st place

380^th place

1auth.gr

9,852^nd place

low place

1escholarship.org

1,523^rd place

976^th place

1academia.edu

121^st place

142^nd place

1ssrn.com

703^rd place

501^st place

1worldcat.org

5^th place

1wisc.edu

1,045^th place

746^th place

1stanford.edu

179^th place

183^rd place

1web.archive.org

1^st place

1opengroup.org

3,671^st place

2,607^th place

1gnu.org

1,475^th place

1,188^th place

academia.edu (Global: 121^st place; English: 142^nd place)

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

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, Niels (1906). Handbuch der Theorie der Gammafunktion (in German). Leipzig: B. G. Teubner. p. 283 Eq. 3. Retrieved 4 December 2017.
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: 69^th place; English: 59^th 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: 9,852^nd 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, Larry C. (1998). Special functions of mathematics for engineers. SPIE Press. p. 110. ISBN 9780819426161.
Glaisher, James Whitbread Lee (July 1871). "On a class of definite integrals". London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 4. 42 (277): 294–302. doi:10.1080/14786447108640568. Retrieved 6 December 2017.
Glaisher, James Whitbread Lee (September 1871). "On a class of definite integrals. Part II". London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 4. 42 (279): 421–436. doi:10.1080/14786447108640600. Retrieved 6 December 2017.

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

Glaisher, James Whitbread Lee (July 1871). "On a class of definite integrals". London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 4. 42 (277): 294–302. doi:10.1080/14786447108640568. Retrieved 6 December 2017.
Glaisher, James Whitbread Lee (September 1871). "On a class of definite integrals. Part II". London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 4. 42 (279): 421–436. doi:10.1080/14786447108640600. Retrieved 6 December 2017.
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.
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
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: 1,523^rd place; English: 976^th 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: 1,475^th place; English: 1,188^th place)

"Special Functions – GSL 2.7 documentation".

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

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

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: 3,671^st place; English: 2,607^th place)

pubs.opengroup.org

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

psu.edu (Global: 207^th place; English: 136^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.
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

semanticscholar.org (Global: 11^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
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: 703^rd place; English: 501^st 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: 179^th place; English: 183^rd 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: 4,963^rd place; English: 7,139^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.

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

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.

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

de.wikipedia.org

Schlömilch, Oskar Xavier (1859). "Ueber facultätenreihen". Zeitschrift für Mathematik und Physik (in German). 4: 390–415.

wisc.edu (Global: 1,045^th place; English: 746^th 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

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

mathworld.wolfram.com

worldcat.org (Global: 5^th place; English: 5^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: 621^st place; English: 380^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: 121st place; English: 142nd place)

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

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

auth.gr (Global: 9,852nd 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: 1,523rd place; English: 976th place)

gnu.org (Global: 1,475th place; English: 1,188th place)

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

ui.adsabs.harvard.edu

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

opengroup.org (Global: 3,671st place; English: 2,607th place)

pubs.opengroup.org

psu.edu (Global: 207th place; English: 136th place)

citeseerx.ist.psu.edu

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

api.semanticscholar.org

ssrn.com (Global: 703rd place; English: 501st place)

stanford.edu (Global: 179th place; English: 183rd place)

wsl.stanford.edu

unibo.it (Global: 4,963rd place; English: 7,139th place)

campus.unibo.it

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

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

de.wikipedia.org

wisc.edu (Global: 1,045th place; English: 746th place)

stat.wisc.edu

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

mathworld.wolfram.com

worldcat.org (Global: 5th place; English: 5th place)

search.worldcat.org

zenodo.org (Global: 621st place; English: 380th place)

academia.edu (Global: 121^st place; English: 142^nd place)

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

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

auth.gr (Global: 9,852^nd place; English: low place)

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

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

escholarship.org (Global: 1,523^rd place; English: 976^th place)

gnu.org (Global: 1,475^th place; English: 1,188^th place)

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

opengroup.org (Global: 3,671^st place; English: 2,607^th place)

psu.edu (Global: 207^th place; English: 136^th place)

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

ssrn.com (Global: 703^rd place; English: 501^st place)

stanford.edu (Global: 179^th place; English: 183^rd place)

unibo.it (Global: 4,963^rd place; English: 7,139^th place)

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

wisc.edu (Global: 1,045^th place; English: 746^th place)

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

worldcat.org (Global: 5^th place; English: 5^th place)

zenodo.org (Global: 621^st place; English: 380^th place)