New Directions For π

Stan Wagon ()
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Stan Wagon: Macalester College, Department of Mathematics and Computer Science

Chapter 18 in Mathematica in Action, 2010, pp 473-490 from Springer

Abstract: Abstract Symbolic computations can lead to unexpected and new formulas for famous constants. The four formulas displayed here (from [AW]) all arose by asking Mathematica to evaluate the abstract expression $$\sum\limits_{k = 0}^\infty {\left({- 4} \right)^{- k} \left({\frac{{a_1}}{{4k + 1}} + \frac{{a_2}}{{4k + 2}} + \frac{{a_3}}{{4k + 3}} + \frac{{a_4}}{{4k + 4}}} \right)} $$ and finding values of the coefficients causing helpful cancellation.

Keywords: Fractional Part; Symbolic Computation; Decimal Digit; Undetermined Coefficient; Correct Digit (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/978-0-387-75477-2_19

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