What identity is given by Ramanujan?
In mathematics, the Rogers–Ramanujan identities are two identities related to basic hypergeometric series and integer partitions. The identities were first discovered and proved by Leonard James Rogers (1894), and were subsequently rediscovered (without a proof) by Srinivasa Ramanujan some time before 1913.
What is used in most in Ramanujan’s theorems?
It was widely used by Ramanujan to calculate definite integrals and infinite series. Higher-dimensional versions of this theorem also appear in quantum physics (through Feynman diagrams).
Who Discovered continued fraction?
The Rogers–Ramanujan continued fraction is a continued fraction discovered by Rogers (1894) and independently by Srinivasa Ramanujan, and closely related to the Rogers–Ramanujan identities. It can be evaluated explicitly for a broad class of values of its argument.
Who created polynomial identities?
§ In the early 16th century, Italian mathematicians Scipone del Ferro, Niccoló Tartaglia, and Gerolamo Cordano were able to solve the general cubic equation in terms of the constants in front of the variables. § Ludovico Ferrari found exact equations for polynomials up to the fourth degree.
What is Ramanujan prime number?
-Ramanujan primes are 11, 29, 59, 67, 101, 149, 157, 163, 191, 227, 269, 271, 307, 379, 383, 419, 431, 433, 443, 457, 563, 593, 601, 641, 643, 673, 701, 709, 733, 827, 829, 907, 937, 947, 971, 1019.
Are continued fractions useful?
The continued fraction representation of the number pi that does follow our rules. When we truncate a continued fraction after some number of terms, we get what is called a convergent. The convergents in a continued fraction representation of a number are the best rational approximations of that number.
How do you find infinite continued fractions?
To calculate a continued fraction representation of a number r, write down the integer part (technically the floor) of r. Subtract this integer part from r. If the difference is 0, stop; otherwise find the reciprocal of the difference and repeat. The procedure will halt if and only if r is rational.
Who is the father of polynomial?
Greek Mathematician Diophantus of Alexandria is the father of polynomials.
What is the identity of a2 b2?
a2 – b2 = (a + b)(a – b ) .