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Unfortunately, I think it is not going to be so easy to source the ""three functions"" part.  I do think it's a pretty good description of actual practice (with a reservation that case (i) is clearer for natural-number exponents, counting 0 as a natural number, than it is for integer exponents).  But there is hardly ever any reason to codify this practice, so finding it in a reliable secondary source may be a challenge.   
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