www.pi314.net

History
Mathematicians
All formulas
Num. approx.
Softwares
Misc. math.
Digits
Poetry
Papers/videos
Delirium !
Pi-Day
Images
Music
 Links
 Bibliography

Boris Gourévitch
The world of Pi - V2.57
modif. 13/04/2013
Google
Home Version history Guestbook Who I am Some pictures (fr) Acknowledgements Last modifications Contact

Cette page en français This page in English

[next page][previous page][bottom previous page][bottom page][table of contents]

8 And the other bases then ? ?

The formulae of the previous section are applicable at all bases 2k and 3k . Good. But it would be great if we could access representation of our favourite constant in other bases !

Unfortunatly, this is for the moment not directly possible with BBP formulae. This is due to the fact that the integrals complicated a lot the task in base 5, 7 or other, by giving some uncomon logarithm or arctan.

Hence, we have for example

oo integral sum 1---1--= 1--5---dy = - 1 V~ 5-ln 2+ 1 V~ 5ln(3 + V~ 5) i=0 5i2i+ 1 0 5 - y2 2 2
 (305)

( ) oo sum (- 1)i 1 integral 1 7 1 V~ V~ 7 -7i--2i+-1 = 7-+-y2dy = 2 7 arctan -3- i=0 0
 (306)

However, we can find certain interesting combination such as this formula by Gery Huvent

oo sum i sum oo ( ) V~ - ---(-1)----+ -1-- --4-- - --1-- = p--6 i=06i+1(2i+ 1) i=0 8i+1 6i+ 1 6i+ 5 12
 (Huvent)

[next page][previous page][bottom previous page][top page][table of contents]

back to home page