# Series expansion around a singular point.

by muppet
Tags: expansion, point, series, singular
 P: 597 Hi All, I have a problem involving some special functions (Meijer-G functions) that I'd like to approximate. At zero argument their first derivative vanishes, but their second and all higher derivatives vanish. (c.f. $f(x)=x^{3/2}$). Playing about with some identities from Gradshteyn and Rhyzik, it looked to me as if this divergence goes like a negative fractional power of the argument, but I can ask Mathematica to give me a series expansion of the function about the origin, wherupon it returns something like: $$f(x) =a + x^2 (b+ c Log[x])+ \ldots$$ where a,b, c are real numbers. How can I compute a "generalised taylor series" of this form analytically myself? Thanks in advance.