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In mathematics, Ramanujan's master theorem, named after Srinivasa Ramanujan, [1] is a technique that provides an analytic expression for the Mellin transform of an analytic function. Page from Ramanujan's notebook stating his Master theorem.
Ramanujan's "Master Theorem" page. Hardy and Littlewood began to look at Ramanujan's notebooks. Hardy had already received 120 theorems from Ramanujan in the first two letters, but there were many more results and theorems in the notebooks. Hardy saw that some were wrong, others had already been discovered, and the rest were new breakthroughs. [94]
In mathematics, the Mellin transform is an integral transform that may be regarded as the multiplicative version of the two-sided Laplace transform.This integral transform is closely connected to the theory of Dirichlet series, and is often used in number theory, mathematical statistics, and the theory of asymptotic expansions; it is closely related to the Laplace transform and the Fourier ...
In mathematics, a theorem that covers a variety of cases is sometimes called a master theorem. Some theorems called master theorems in their fields include: Master theorem (analysis of algorithms), analyzing the asymptotic behavior of divide-and-conquer algorithms; Ramanujan's master theorem, providing an analytic expression for the Mellin ...
Ramanujam vanishing theorem (algebraic geometry) Ramanujan–Skolem's theorem (Diophantine equations) Ramsey's theorem (graph theory, combinatorics) Rank–nullity theorem (linear algebra) Rao–Blackwell theorem ; Rashevsky–Chow theorem (control theory) Rational root theorem (algebra, polynomials) Rationality theorem
Ramanujan's master theorem; Riemann–Siegel formula; Riemann–von Mangoldt formula; S. Siegel–Walfisz theorem; V. Vaughan's identity; Vinogradov's mean-value theorem
Ramanujan tau function; Ramanujan theta function; Ramanujan–Nagell equation; Ramanujan–Petersson conjecture; Ramanujan–Sato series; Ramanujan–Soldner constant; Ramanujan's congruences; Ramanujan's lost notebook; Ramanujan's master theorem; Ramanujan's sum; Ramanujan's ternary quadratic form; Rank of a partition; Rogers–Ramanujan ...
In mathematics, Ramanujan's Master Theorem (named after Srinivasa Ramanujan [1]) is a technique that provides an analytic expression for the Mellin transform of an analytic function. Page from Ramanujan's notebook stating his Master theorem. The result is stated as follows: If a complex-valued function () has an expansion of the form