NumCosmoMathLaurentSeriesTPSpow

Raises the truncated power series $a(g)$ to the real power p: $out(g)=a(g)^p \mod g^{N+1}$. Only a plain gdouble exponent is supported (not complex double): every current use (e.g. NcGalaxyShapePopBeta‘s own $\rho^{2(\alpha-1)}$ composition) only ever needs a real exponent, and restricting to real keeps this fully introspectable (no native-only guard needed at all).

$a$ must have $a_0\ne0$: factor $a(g)=a_0(1+u(g))$ with $u(0)=0$, then $(1+u)^p=\sum_n c_n g^n$ ($c_0=1$) follows the generalized-binomial recursion $n c_n=\sum_{k=1}^n[kp-(n-k)]u_k c_{n-k}$ (from differentiating $F=(1+u)^p$: $(1+u)F’=p u’F$), and $out=a_0^p\,\sum_n c_n g^n$.