1. For non-integer ?, a more general power series expansion is required. 2. :: There must be more fancy power series expansions for the logarithm which converge faster. 3. Where the power series expansion for about follows because has a simple pole of residue one there. 4. You have a well defined and convergent power series expansion about each point of the complex plane. 5. In light of the power series expansion , it is not surprising that Liouville's theorem holds. 6. Since none of the functions discussed in this article are continuous, none of them have a power series expansion . 7. Moreover, the power series expansion of a holomorphic function in \ mathcal F gives its expansion with respect to this basis. 8. The singularities nearest 0, which is the center of the power series expansion , are at ?? " i ". 9. This condition is imposed by demanding that no odd powers of " t " appear in the formal power series expansion : 10. Again, the function " x x " have well defined power series expansions at each point of the positive real numbers.
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