How many formulas Ramanujan have?

How many formulas Ramanujan have?

Chan, and S. –S. Huang [25] found proofs for all of Ramanujan’s approximately 15 formulas employing only results from Ramanu- jan’s notebooks [61] and lost notebook [62]. See also Chapter 15 of our book [10].

Where is Ramanujan formula used?

American researchers now say Ramanujan’s formula could explain the behaviour of black holes, the Daily Mail reported. “We have solved the problems from his last mysterious letters. For people who work in this area of math, the problem has been open for 90 years” Emory University mathematician Ken Ono said.

Is Ramanujan summation correct?

“Ramanujan summation” is a way of assigning values to divergent series. As such, it isn’t true or false, just defined (or not, as the case may be). This particular case really does “work”. However, the left-hand side should say that it’s a Ramanujan summation, not a regular “sum of a series”, and it doesn’t.

What is Ramanujan’s magic square?

In recreational mathematics, a magic square of order n is an arrangement of n2 numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. A normal magic square contains the integers from 1 to n2.

Why is 1729 a magic number?

It is 1729. Discovered by mathemagician Srinivas Ramanujan, 1729 is said to be the magic number because it is the sole number which can be expressed as the sum of the cubes of two different sets of numbers. Ramanujan’s conclusions are summed up as under: 1) 10 3 + 9 3 = 1729 and 2) 12 3 + 1 3 = 1729.

Who was invented zero?

About 773 AD the mathematician Mohammed ibn-Musa al-Khowarizmi was the first to work on equations that were equal to zero (now known as algebra), though he called it ‘sifr’. By the ninth century the zero was part of the Arabic numeral system in a similar shape to the present day oval we now use.

What are the solutions of the Ramanujan-Nagell equation?

sometimes called the Ramanujan-Nagell equation, has any solutions other than , 4, 5, 7, and 15 (Schroeppel 1972, Item 31; Ramanujan 2000, p. 327; OEIS A060728 ). These correspond to , 3, 5, 11, and 181 (OEIS A038198 ).

What is the Ramanujan summation?

For those of you who are unfamiliar with this series, which has come to be known as the Ramanujan Summation after a famous Indian mathematician named Srinivasa Ramanujan, it states that if you add all the natural numbers, that is 1, 2, 3, 4, and so on, all the way to infinity, you will find that it is equal to -1/12. Yup, -0.08333333333.

How many solutions to Ramanujan’s question are There?

These correspond to , 3, 5, 11, and 181 (OEIS A038198 ). Nagell (1948) and Skolem et al. (1959) showed there are no solutions past , thus establishing Ramanujan’s question in the negative.

What is the Ramanujan-type formula for Pi?

A Ramanujan-type formula due to the Chudnovsky brothers used to break a world record for computing the most digits of pi: For implementations, it may help to use 6403203 =8 ⋅100100025 ⋅327843840 640320 3 = 8 ⋅ 100100025 ⋅ 327843840

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