# Search Results for ""

1 - 10 of 214 for ramanujan biographySearch Results

There are two awards that each go by the name "

**Ramanujan**Prize": the SASTRA**Ramanujan**Prize and the ICTP**Ramanujan**Prize for Young Mathematicians from Developing Countries. ...The nth

**Ramanujan**prime is the smallest number R_n such that pi(x)-pi(x/2)>=n for all x>=R_n, where pi(x) is the prime counting function. In other words, there are at least n ...In 1913,

**Ramanujan**asked if the Diophantine equation of second order 2^n-7=x^2, sometimes called the**Ramanujan**-Nagell equation, has any solutions other than n=3, 4, 5, 7, and ...The irrational constant R = e^(pisqrt(163)) (1) = 262537412640768743.9999999999992500... (2) (OEIS A060295), which is very close to an integer. Numbers such as the

**Ramanujan**...Following

**Ramanujan**(1913-1914), write product_(k=1,3,5,...)^infty(1+e^(-kpisqrt(n)))=2^(1/4)e^(-pisqrt(n)/24)G_n (1) ...The Rogers-

**Ramanujan**continued fraction is a generalized continued fraction defined by R(q)=(q^(1/5))/(1+q/(1+(q^2)/(1+(q^3)/(1+...)))) (1) (Rogers 1894,**Ramanujan**1957, ...The smallest nontrivial taxicab number, i.e., the smallest number representable in two ways as a sum of two cubes. It is given by 1729=1^3+12^3=9^3+10^3. The number derives ...

A sum which includes both the Jacobi triple product and the q-binomial theorem as special cases.

**Ramanujan's**sum is ...For |q|<1, the Rogers-

**Ramanujan**identities are given by (Hardy 1999, pp. 13 and 90), sum_(n=0)^(infty)(q^(n^2))/((q)_n) = 1/(product_(n=1)^(infty)(1-q^(5n-4))(1-q^(5n-1))) ...The two-argument

**Ramanujan**function is defined by phi(a,n) = 1+2sum_(k=1)^(n)1/((ak)^3-ak) (1) = 1-1/a(H_(-1/a)+H_(1/a)+2H_n-H_(n-1/a)-H_(n+1/a)). (2) The one-argument ......