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What are some of Ramanujan's craziest formulas?

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I would like to share a story I have heard about Ramanujan and yes it is enough crazy to share here. Once Ramanujan was admitted to hospital, he was sick. His mentor and a great mathematician Mr. Hardy went to see him. Mr. Hardy said, 'The number of the taxi I came by is 1729 how uncool number is that!'. read more

which is simply the usual integral formula for the gamma function. Here is mathematical explanation: Ramanujan's Master Theorem The theorem is an analytical expression for the Mellin transform of a function and it is widely used to calculate definite integrals and infinite series. read more

There are direct formulas to calculate $a, b, c$ and we have two forms of such formulas. One of the forms is a finite formula which may require computations of algebraic nature (so that effectively the value is expressible as a radical expression). read more

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Book Excerptise: Ramanujan: Twelve Lectures on Subjects ...
Source: cse.iitk.ac.in