Expand a Function with Taylor Series: Quick & Easy

MMS
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Hi guys,

Is there an easy and quick way to expand a function that I know its Taylor series about 0 to a series about some other z_0?
 
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Not really. That would imply a quick and easy way to express ##f^{(k)}(z_0)## in terms of the Taylor series at 0. You can do it of course, but it just gives you an expression for each of these as a (different) power series in ##z_0##, and while the calculation is straightforward presumably this isn't what you have in mind.
Think about it: even if the power series if finite (polynomial), it is rather cumbersome.
 
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A sphere as topological manifold can be defined by gluing together the boundary of two disk. Basically one starts assigning each disk the subspace topology from ##\mathbb R^2## and then taking the quotient topology obtained by gluing their boundaries. Starting from the above definition of 2-sphere as topological manifold, shows that it is homeomorphic to the "embedded" sphere understood as subset of ##\mathbb R^3## in the subspace topology.

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