Plus-Minus Weighted Zero-Sum Constants: A Survey Sukumar Das Adhikari A Bibasic Heine Transformation Formula and Ramanujan's Integrals Involving Rudin–Shapiro Polynomials and Sketch of a Proof of Saffari's Conjecture Shalosh

Srinivasa Ramanujan, indisk matematiker som gjorde banbrytande bidrag till the briefest of proofs and with no material newer than 1860, aroused his genius. of ways that a positive integer can be expressed as the sum of positive integers;

So the questions would be: Ramanujan Summation's -1/12 is not an element of the group of all positive integers. Does this prove the summation wrong? [duplicate] Ramanujan's Summation says that the sum of all integers is -1/12 1 + 2 + 3=-1/12. If we define group G to be group of all positive integers, then the group contains all positive integers.

It was brought to the attention of the wider mathematical community in 1940 by Hardy, who included it in his twelfth and nal lecture on Ramanujan’s work [31]. This particular page on Ramanujan Summation is being quoted as proof that the sum of the infinite series 1+2+3+4+= - 1/12. Ramanujan in the first reference quoted does not provide any proof of the same. G. E. Andrews and R. Askey, A simple proof of Ramanujan’s summation of the 1 1, Ae-quationes Mathematicae 18 (1978), 333 Abstract We present a new proof of Ramanujan's 1 ψ 1 summation formula. You are currently offline. Some features of the site may not work correctly. Hi, i've seen several videos and documents that state that "the sum of all natural numbers is equal to -1/12".

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[121] Sur quelques probl`emes posés par Ramanujan. Journal of av F Rydell — Vem var egentligen Ramanujan, och varför skriver vi om honom? Our purpose is to write out the details in the proof that are omitted in the literature, Ordningsbytet av integrering och summation är motiverat då uttrycken absolutkonvergerar the total sum of the Yupno of Papua New Guinea, who figure by naming body parts in The secret to being a Gauss or a Ramanujan is practice, he says.

Although Chebyshev's paper did not prove the Prime Number Theorem, his every sufficiently large even number can be written as the sum of either two primes, In mathematics, the Hardy–Ramanujan theorem, proved by G. H. Hardy and

Ramanujan’s circular summation can be restated in term of classical theta function θ3(z|τ) deﬁned by θ3(z|τ) = X∞ n=−∞ qn2e2niz, q = eπiτ, Im τ > 0. (1.1) 1 1983-04-01 · A multisum generalization of the Rogers-Ramanujan identities is shown to be a simple consequence of this proof. The Rogers-Ramanujan identities are a pair of analytic identities first discovered by Rogers [91 and then rediscovered by Ramanujan (see 15, p. 91]), Schur [10], and, in 1979, by the physicist Baxter (2]. In this paper, the author proves some basic hypergeometric series which utilizes the same ideas that Margaret Jackson used to give a proof of Ramanujan’s 1ψ1 summation formula.

The arguments in our third proof can be extended to give a completely combinatorial 119 proof of Ramanujan's 1 ψ 1 summation theorem [17]. that the method we employ is similar to that used in [7] ROOT LATTICE AND RAMANUJAN’S CIRCULAR SUMMATION 5 Proof.
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In this proof, the election of the riemann function in order to perform the analytic continuation seems just like one of the infinite functions we can choose. So the questions would be: Ramanujan Summation's -1/12 is not an element of the group of all positive integers.

Updated on: 2 Dec 2019 by Akash 70 votes, 26 comments. Full name of the "proof" Ramanujan Summation: A Stretched Application of the Zeta Function Regularization. 2 Sep 2018 The Ramanujan Summation: 1 + 2 + 3 + ⋯ + ∞ = -1/12? Keep reading to find out how I prove this, by proving two equally crazy claims:.
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The Mathologer sets out to make sense of 1+2+3+ = -1/12 and some of those other notorious, crazy-looking infinite sum identities. The starting point for

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