Hi everybody!
I'm interessed in the behavior near zero of a function depending on a positive parameter"p":
Cas2a[\[Phi]_] :=
Sqrt[-((p + (1 + p) (-1 + (1/(1 + p))^\[Phi]) \[Phi] PolyGamma[
1, \[Phi]])/(p (1 + p)^2 \[Phi]^2))];
(Phi should be positive too). So, I compute the beginning of the series near 0:
Series[Cas2a[\[Phi]], {\[Phi], 0, 1}]
Print[Style["Coef order -1 =", Bold, Blue],
SeriesCoefficient[Series[Cas2a[\[Phi]], {\[Phi], 0, 1}], -1]];
Print[Style["Coef order 0 =", Bold, Blue],
SeriesCoefficient[Series[Cas2a[\[Phi]], {\[Phi], 0, 1}], 0]]; Print[
Style["Coef order 1 =", Bold, Blue],
SeriesCoefficient[Series[Cas2a[\[Phi]], {\[Phi], 0, 1}], 1]];
there is a lag in the coefficient! On the contrary, processing a simpler function, there is no problem.
Series[Cos[x]/x, {x, 0, 10}]
Table[SeriesCoefficient[Series[Cos[x]/x, {x, 0, 10}], i], {i, -1, 3}]
Why? What should I do? Thanks in advance, Claude