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

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

1oeis.org

742^nd place

538^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

1harvard.edu

18^th place

17^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

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

archive.org

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

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. 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. 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

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

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

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.
Ng, Edward W.; Geller, Murray (January 1969). "A table of integrals of the Error functions". Journal of Research of the National Bureau of Standards Section B. 73B (1): 1. doi:10.6028/jres.073B.001.
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. 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. 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. 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. 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.
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. doi:10.1109/TCOMM.2020.2986209. S2CID 216500014.

escholarship.org

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. doi:10.1109/TCOMM.2011.072011.100049. S2CID 13636638.

gnu.org

"Special Functions – GSL 2.7 documentation".

harvard.edu

ui.adsabs.harvard.edu

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

mathematica-journal.com

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.

oeis.org

"A007680 – OEIS". oeis.org. Retrieved 2 April 2020.

opengroup.org

pubs.opengroup.org

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

psu.edu

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. 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

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. 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. 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. 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. doi:10.1109/TCOMM.2020.2986209. S2CID 216500014.