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Boris Gourévitch
The world of Pi - V2.57
modif. 13/04/2013



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15 Other hypergeometric formulae concerning p

There exist loads of hypergeometric formulae linked to p  , for example

   (     1   3 )
3F2   1,-94,1-1 4   = 21p
        4,4-       64
(715)

that I've found, or

        (    1 1 )
4-  8.3F2   1,52,52   = p
    9       2,2
(716)

that I've read. The formulae by Ramanujan or Chudnovsky can equally be written under the form of hypergeometric functions. The problem is to not loose yourself in the coefficients, the hypergeometric formulae have a few too many free parameters! Basicly impossible to find an easy generalisation in all of those this.

Conclusion 27 Of course, this page is to evolve according to my courage, my last findings, or even your ideas or contribution! My first objective was to showw you how a certain form of integral, which is very often equivalent to a hypergeometric series, can give a familly of constant that we understand more now: p,ln(k),G,z(k),  etc...
This current subject will without doubt be more clear and unified in the following years. It doesn't have to be that hard (at least how I presented it! ) but this does show some really promosing leads, numerous and sometime a bit forgotten by our dear mathematicians!


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