Search results
Results From The WOW.Com Content Network
Ramanujan's sum. In number theory, Ramanujan's sum, usually denoted cq ( n ), is a function of two positive integer variables q and n defined by the formula. where ( a, q) = 1 means that a only takes on values coprime to q . Srinivasa Ramanujan mentioned the sums in a 1918 paper. [ 1]
In number theory, the partition function p(n) represents the number of possible partitions of a non-negative integer n. For instance, p(4) = 5 because the integer 4 has the five partitions 1 + 1 + 1 + 1, 1 + 1 + 2, 1 + 3, 2 + 2, and 4 . No closed-form expression for the partition function is known, but it has both asymptotic expansions that ...
Ramanujan–Sato series. In mathematics, a Ramanujan–Sato series[ 1][ 2] generalizes Ramanujan ’s pi formulas such as, to the form. by using other well-defined sequences of integers obeying a certain recurrence relation, sequences which may be expressed in terms of binomial coefficients , and employing modular forms of higher levels.
Srinivasa Ramanujan[ a] (22 December 1887 – 26 April 1920) was an Indian mathematician. Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems then considered unsolvable.
In mathematics, the Ramanujan conjecture, due to Srinivasa Ramanujan ( 1916 , p. 176), states that Ramanujan's tau function given by the Fourier coefficients τ(n) of the cusp form Δ (z) of weight 12. where , satisfies. when p is a prime number.
1729 (number) 1729 is the natural number following 1728 and preceding 1730. It is the first nontrivial taxicab number, expressed as the sum of two cubic numbers in two different ways. It is also known as the Ramanujan number or Hardy–Ramanujan number, named after G. H. Hardy and Srinivasa Ramanujan .
The Ramanujan tau function, studied by Ramanujan ( 1916 ), is the function defined by the following identity: where q = exp (2πiz) with Im z > 0, is the Euler function, η is the Dedekind eta function, and the function Δ (z) is a holomorphic cusp form of weight 12 and level 1, known as the discriminant modular form (some authors, notably ...
Ramanujan summation is a method of assigning a value to divergent series used by Ramanujan and based on the Euler–Maclaurin summation formula. The Ramanujan sum of a series f (0) + f (1) + ... depends not only on the values of f at integers, but also on values of the function f at non-integral points, so it is not really a summation method in ...