User:Zeraouliarafik15/Zeraoulia function ,New special function and its application in probability

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Definition of Zeraoulia function

Zeraoulia function is a new special function see ^[1] , ^[2] proposed by Zeraoulia Rafik in 17/02/2017 and have been studied by Zeraoulia rafik, Alvaro Humberto Salas , davide L.Ocampo and published in ^[3], it behave like more than Error function and it is defined as :

$T(a)=\int _{0}^{a}{(e^{-x^{2}})}^{\operatorname {erf} (x)}dx$ mathematica gives for the first $100$ digits:

$T(\infty )=0.9721069927691785931510778754423911755542721833855699009722910408441888759958220033410678218401258734$ with $T(0)=0$

References

^ E. W. Ng and M. Geller, “A table of integrals of the error functions,” Journal of Research of the National Bureau of Standards, vol. 73B, pp. 1–20, 1969
^ E. W. Ng and M. Geller, “A table of integrals of the error functions,” Journal of Research of the National Bureau of Standards, vol. 73B, pp. 1–20, 1969. View at Google Scholar · View at MathSciNet
^ Zeraoulia Rafik, Alvaro H. Salas, and David L. Ocampo, “A New Special Function and Its Application in Probability,” International Journal of Mathematics and Mathematical Sciences, vol. 2018, Article ID 5146794, 12 pages, 2018. https://doi.org/10.1155/2018/5146794

External links

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[1] E. W. Ng and M. Geller, “A table of integrals of the error functions,” Journal of Research of the National Bureau of Standards, vol. 73B, pp. 1–20, 1969

[2] E. W. Ng and M. Geller, “A table of integrals of the error functions,” Journal of Research of the National Bureau of Standards, vol. 73B, pp. 1–20, 1969. View at Google Scholar · View at MathSciNet

[3] Zeraoulia Rafik, Alvaro H. Salas, and David L. Ocampo, “A New Special Function and Its Application in Probability,” International Journal of Mathematics and Mathematical Sciences, vol. 2018, Article ID 5146794, 12 pages, 2018. https://doi.org/10.1155/2018/5146794

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