The hyperelliptic integrals and π

Mingari Scarpello, Giovanni ; Ritelli, Daniele (2009) The hyperelliptic integrals and π. Journal of Number Theory, 129 (12). pp. 3094-3108. ISSN 0022-314X
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A class of hyperelliptic integrals are expressed through hypergeometric functions, like those of Gauss, Lauricella and Appell, namely multiple power series. Whenever they can on their own be reduced to elliptic integrals through an algebraic transformation, we obtain a two-fold representation of the same mathematical object, and then several completely new π determinations through the above special functions and/or Euler integrals.AllourπformulaehavebeensuccesfullytestedbymeansofconvenientMathematica’s packages and enter in a wide historical/sound context of π- formulae quite far from being exhausted. Due to their structure, the formulae’s practical value does not lie in computing π, but in allowing, through π, a benchmark for computing the involved special functions, particularly those less elementary.

Document type
Mingari Scarpello, Giovanni
Ritelli, Daniele
Complete Elliptic Integral of first kind, Hypergeometric Function, π, Appell Function, Lauricella- Saran Function
Deposit date
16 Sep 2011 07:25
Last modified
16 Sep 2011 07:25

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