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On Jackson’s proof of Ramanujan’s 1ψ1 summation formula @article{Villacorta2017OnJP, title={On Jackson’s proof of Ramanujan’s 1ψ1 summation formula}, author={Jorge Luis Cimadevilla Villacorta}, journal={International Journal of Number Theory}, year={2017}, volume={14}, pages={313-328} } The third video in a series about Ramanujan.This one is about Ramanujan Summation. Here's the wikipedia page for further reading: https://en.wikipedia.org/wi In this paper, we give a completely elementary proof of Ramanujan’s circular summation formula of theta functions and its generalizations given by S.H. Chan and Z.-G. Liu, who used the theory of elliptic functions. In contrast to all other proofs, our proofs are elementary. An application of this summation formula is given. This video will make you think how the sum of all natural numbers came negative. THINK The Most Controversial Topic In Mathematics (Ramanujan Summation) Hello everyone!! Hope you all are well.

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Eddie Woo. 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;  I Scientific American, februari 1988, finns en artikel om Ramanujan och π d¨ ar man Newman, D. J., Simple analytic proof of the prime number theorem. Summation motsvarar integration, och m˚ anga formler liknar varandra, t ex de f¨ or  The Ramanujan Summation: 1 + 2 + 3 + ⋯ + ∞ = -1/12? | by Easy as 1, 2, 3.

av A Söderqvist — There has been some advances in proof checkings and even even number is the sum of two primes, it must be very close to one.

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He then moved into Whewell's Court at Trinity. The Ramanujan Summation: 1 + 2 + 3 + ⋯ + ∞ = -1/12?The infinite series whose terms are the natural numbers 1 + 2 + 3 + 4 + ⋯ is a divergent series. The nth p DOI: 10.1142/S1793042118500197 Corpus ID: 125410204. On Jackson’s proof of Ramanujan’s 1ψ1 summation formula @article{Villacorta2017OnJP, title={On Jackson’s proof of Ramanujan’s 1ψ1 summation formula}, author={Jorge Luis Cimadevilla Villacorta}, journal={International Journal of Number Theory}, year={2017}, volume={14}, pages={313-328} } The third video in a series about Ramanujan.This one is about Ramanujan Summation.

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What most surprised me is discovering that the Ramanujan summation is used in string theory and quantum mechanics. If I am right and the sum is actually –3/32, then we are in trouble here, because this implies that some statements of string theory are based on an incorrect result. A Ramanujan-type formula due to the Chudnovsky brothers used to break a world record for computing the most digits of pi: 1 π = 1 53360√640320 ∞ ∑ n=0(−1)n (6n)!

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 Srinivasa Ramanujan FRS (/ ˈ s r ɪ n ɪ v ɑː s r ɑː ˈ m ɑː n ʊ dʒ ən / ; born Srinivasa Ramanujan Aiyangar ; 22 December 1887 – 26 April 1920) was an Indian mathematician who lived during the British Rule in India. Though he had almost no formal training in pure mathematics , he made substantial contributions to mathematical analysis , number theory , infinite series , and Since Ramanujan’s 1ψ1 sum was first brought before the mathematical public by Hardy[3] in 1940 and first proved by Hahn [4] and Jackson [5] respectively, to find any possible elegant and simple proof of this identity has still been a charming problem in the theory of q-series.
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Disproof of some conjectures of K. Ramachandra, Hardy-Ramanujan. 1976: Appel and Haken prove the Four Colour Conjecture using a computer. 1977: Adelman, Rivest and Shamir introduce public-key cryptography using prime  Ramanujan's Lost Notebook: Part II: Andrews, George E.: Amazon.se: Books. 3 Ramanujan's Proof of the q-Gauss Summation Theorem . .

Butterworth sees the international comparisons he cites as proof that children can  Ramanujan Journal. Vol. 13, p.
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. . 94 but thanks to the Ramanujan summation we can prove simply that this function G2  This provides simple proofs of theorems on the summation of some divergent series. Several examples and applications are given. For numerical evaluation, a   A simple proof by functional equations is given for Ramanujan's1 ψ 1 sum. Ramanujan's sum is a useful exte.

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Watson [25] utilized partial fractions to prove some of Ramanujan’s theoremsonmockthetafunctions.Inthepastfewyears,ithasbecomeincreasinglyapparent that Ramanujan employed partial fractions in proving theorems in the theory of q-series, Se hela listan på scienceabc.com Srinivasa Ramanujan mentioned the sums in a 1918 paper.

It's in the work of pioneering Indian mathematician Srinivasa Ramanujan, for instance: We haven't even attempted to tackle to long proofs involved in sorting ou 1 Apr 2015 Ramanujan discusses this series in one of his magical notebooks.