Explicit Ramanujan-type approximations to pi of high order
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We combine previously developed work with a variety of Ramanujan’s higher order modular equations to make explicit, in very simple form, algebraic approximations to π which converge with orders including 7, 11, 15 and 23.
KeywordsRamanujan-type approximations recursive approximation to pi
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- Berndt B C,Chapters 19 and 20 of Ramanujan’s second notebook (Springer Verlag) (to appear)Google Scholar
- Borwein J M, Borwein P B and Bailey D H, Ramanujan, modular equations and pi: or how to compute a billion digits of pi,M A A Monthly (in press)Google Scholar
- Hardy G H,Ramanujan’s collected papers (New York: Chelsea Publishing) (1962)Google Scholar
- Magnus W, Formulae and theorems for the special functions of mathematical physics (Berlin: Springer Verlag) (1966)Google Scholar
- Ramanujan S, Modular equations and approximations to π,Q. J. Math. Oxford 45 (1914) 350–372 (New York: Chelsea) (1980)Google Scholar
- Weber H,Lehrbuch der algebra (Baruschweig) vol. 3 (1908)Google Scholar