In this note we present a new special function that behaves like the error function and we provide an aproximated accurate closed form for it’ s CDF in terms of both Chebyshev polynomials of the first kind and the error function.Also we provide it’s series representation using pade approximant , We show a convincing numerical evidence about an accuracy of 10^(-6) for the approximants in the sense of the quadratic mean norm. A similar approach may be applied to other probability distributions.
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[v1] 2018-06-24 18:43:03
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