Series and Product Representations
The identity, along with the infinite product representations for the sine and cosine, leads to products such as
and
or equivalently,
The number can also be expressed by taking the Taylor series of a trigonometric function. For example, the series for gives
The Taylor series of with and using the double factorial gives
The convergence of this series can be accelerated with an Euler transform, producing
It is not known whether can be represented with a BBP-type formula. BBP-type formulas are known for π and ), however.
Read more about this topic: Square Root Of 2
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