What are the formulas given by Ramanujan?

In mathematics, in the field of number theory, the Ramanujan–Nagell equation is an equation between a square number and a number that is seven less than a power of two. It is an example of an exponential Diophantine equation, an equation to be solved in integers where one of the variables appears as an exponent.

What is the secret of Ramanujan?

Ramanujan believed that 17 new functions he discovered were “mock modular forms” that looked like theta functions when written out as an infinte sum (their coefficients get large in the same way), but weren’t super-symmetric.

Which symbol is used in Ramanujan’s theory?

where Γ(s) denotes the gamma function. It was widely used by Ramanujan to calculate definite integrals and infinite series.

Did Srinivasa Ramanujan believe in God?

A deeply religious Hindu, Ramanujan credited his substantial mathematical capacities to divinity, and said the mathematical knowledge he displayed was revealed to him by his family goddess Namagiri Thayar. He once said, “An equation for me has no meaning unless it expresses a thought of God.”

What is the Hardy-Ramanujan number?

The Hardy-Ramanujan number is “1729”. It is the smallest number expressible as the sum of two positive cubes in two different ways. The two different ways are: Clearly adding up the two numbers in both the cases gives us 1729.

What is the significance of the equation of Ramanujan?

The equation of Ramanujan illustrates that he had found an infinite family of positive whole number triples x, y and z that very nearly, but not quite, satisfy Fermat’s equation for n=3. They are off only by plus or minus one. Among them is 1729, which misses the mark by 1 for x=9, y=10 and z=12.

How did Ramanujan get the number 1103 and 26390?

Ramanujan himself got this formula by remaining within the limits of real analysis and I have presented these ideas along with proofs in my blog post. Please note that the actual calculation to obtain the numbers 1103 and 26390 in the formula is difficult.

What is the Ramanujan type of congruence?

The study of Ramanujan type congruence is a popular research topic of number theory. It was in 2011, that a conceptual explanation for Ramanujan’s congruences was finally discovered. Ramanujan’s work on partition theory has applications in a number of areas including particle physics (particularly quantum field theory) and probability.