Mathematica doesn't expand the series of this function (I'm using Wolfram Cloud version)


Is there any other method to do it?


1 Answer 1


One solution is to drop all terms in the definition of ϕ that do not affect the series expansion up to the requested order:

With[{n=10}, Series[ϕ[z,n]/(1-ϕ[z,n]),{z,0,n}]]

(* z+z^2+3 z^3+4 z^4+7 z^5+14 z^6+23 z^7+39 z^8+71 z^9+124 z^10+O[z]^11 *)

See also A003242.


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