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Srinivasa Ramanujan mentioned the sums in a 1918 paper. [1] In addition to the expansions discussed in this article, Ramanujan's sums are used in the proof of Vinogradov's theorem that every sufficiently large odd number is the sum of three primes. [2]
Ramanujan summation is a technique invented by the mathematician Srinivasa Ramanujan for assigning a value to divergent infinite series.Although the Ramanujan summation of a divergent series is not a sum in the traditional sense, it has properties that make it mathematically useful in the study of divergent infinite series, for which conventional summation is undefined.
Ramanujan summation is a method to isolate the constant term in the Euler–Maclaurin formula for the partial sums of a series. For a function f , the classical Ramanujan sum of the series ∑ k = 1 ∞ f ( k ) {\displaystyle \textstyle \sum _{k=1}^{\infty }f(k)} is defined as
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The Ramanujan Journal; Ramanujan Math Park; Ramanujan Mathematical Society; Ramanujan prime; Ramanujan summation; 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 ...
“Blue Bloods” is saying goodbye to two special men: Treat Williams and his character, Lenny Ross. The former partner of New York Police Commissioner Francis “Frank” Reagan, played by Tom ...
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.
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