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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. [itex]f(x)=x^{3/2}[/itex]). 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:

[tex]f(x) =a + x^2 (b+ c Log[x])+ \ldots [/tex]

where a,b, c are real numbers.

How can I compute a "generalised taylor series" of this form analytically myself?

Thanks in advance.

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# Series expansion around a singular point.

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