Taylor series application of Gaussian Distribution. How come???

lks

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Φ(z)= ∫(z from -∞ to z)exp (- (x)^2/2)/(2Π)^ (-0.5)dz = 1 / 2 + φ(z) Σ(((z)^k)/ (k!!))
the Φ(z) is the integration of φ(z) from -∞ to z,
and the σ is 1, and the μ is 0.
the sequence of series of Σ(((z)^k)/ (k!!)) is like this below
z + z^3/3 + z^5/(3 * 5) + z^7*(3*5*7)...etc
 
the pic shows it more clearly
 

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