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in that example we used the geometric series:formula_4and the weierstrass m-test to demonstrate that the simple example defines an analytic function on the open unit disk.
in that example we used the geometric series:formula_9and the weierstrass m-test to demonstrate that the simple example defines an analytic function on the open unit disk.

* lata mangeshkar best singer award for 2011 was presented by the state government at "2nd lata mangeshkar music awards - 2011" function on september 28, 2011 at ravindra bharathi, hyderabad.
* ghantasala melody queen award in 2011* lata mangeshkar best singer award for 2011 was presented by the state government at "2nd lata mangeshkar music awards – 2011" function on 28 september 2011 at ravindra bharathi, hyderabad.

this operation is compatible with differentiation in the sense that:formula_29and also with convolution: if "s" is a tempered distribution and ψ is a "slowly increasing" infinitely differentiable function on r"n" (meaning that all derivatives of ψ grow at most as fast as polynomials), then "s"ψ is againa tempered distribution andis the convolution of "fs" and "f"ψ.
this operation is compatible with differentiation in the sense that:formula_49and also with convolution: if "t" is a tempered distribution and "Ψ" is a "slowly increasing" infinitely differentiable function on r"n" (meaning that all derivatives of "Ψ" grow at most as fast as polynomials), then "ψt" is againa tempered distribution and:formula_50is the convolution of "ft" and "fψ".