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Can I turn any multivariate function into polinomial series in Mathematica?

Suppose I have a function

Fwd[x_, α_] := x (1/Sin[Pi x/2])^α

and wish to express it with a formula, consisting only of multiplications and summations. Is it possible?

If I apply

Normal[Series[Fwd[x, α], {x, 0, 3}, {α, 0, 3}]]

I get complex formula

enter image description here

which contains Log function. Why?

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You get log because:

Fwd[x_,\[Alpha]_]:=x (1/Sin[Pi x/2])^\[Alpha] = x* Exp[\[Alpha]*Log[1/Sin[Pi x/2]]]

and the log is from the expansion with respect to alpha.

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