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The Reciprocal of Infinite Product

The Reciprocal of Infinite Product

 

The reciprocal of the beautiful infinite product of nested radicals due to Vieta in 1592 is decomposed into partial fractions of the infinite series as shown below.

            , in which

.

 

 

 


The mathematical sciences particularly exhibit order, symmetry,

and limitation; and these are the greatest forms of the beautiful.

                                                                                                                                                  Aristotle

 

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