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Results tagged with ramanujan
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user 32389
37
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5
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How did Ramanujan discover this identity?
Let $$\small F_n=(a+b+c)^n+(b+c+d)^n-(c+d+a)^n-(d+a+b)^n+(a-d)^n-(b-c)^n$$ and
$ad=bc$, then
$$64 F_6 F_{10}=45 F_8^2$$
This fascinating identity is due to Ramanujan and can be found in "Ramanujan for … Would anyone have any idea how Ramanujan discovered this identity?
The proofs of the identity offered so far in the papers "A Note on an Identity of Ramanujan", by T. S. …
- 16.5k
10
votes
Accepted
Ramanujan's pi formulas with a twist
Almkvist), http://arxiv.org/abs/0712.1332 (Ramanujan-type formulae for 1/π: A second wind? … , by Wadim Zudilin) and http://arxiv.org/abs/1302.0548 (Ramanujan-type formulae for 1/π: the art of translation, by Jesus Guillera and Wadim Zudilin). …
- 16.5k
4
votes
How did Ramanujan prove this congruence?
As Berndt&Ono publication shows, in fact Ramanujan was well aware of this fact. … Hardy in his book "Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work" also states that it was Ramanujan who proved the congruence and refers to the article of G.N. …
- 16.5k