- #1
muppet
- 608
- 1
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. [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.
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.