26 Aug 2019 Pythagoras NewtonGaussEuclid CGauss is the famous mathematician associated with finding the sun of the first 100 natural number i.e.,

In this video lecture we will discuss the proof of Ramanujan summation of natural numbers 1+2+3+4…..=-1/12. Ramanujan wrote a letter to Cambridge mathematician G.H Hardy and in the 11 page letter there were a number of interesting results and proofs and after reading the letter Hardy was surprised about the letter that changed the face of mathematics forever.

One thing that can be said is that Ramanujan based this discovery upon the already proven series 1+1-1+1-1+1 = 1/2 If you think about this series you can perceive that the value 1/2 is not the summation because the summation value alters infinitely between 1 and 0. The aim of this monograph is to give a detailed exposition of the summation method that Ramanujan uses in Chapter VI of his second Notebook. This method, presented by Ramanujan as an application of the Euler-MacLaurin formula, is here extended using a difference equation in a space of analytic functions. This provides simple proofs of theorems on the summation of some divergent series. Several 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)! n!3(3n)! × 13591409+545140134n 6403203n 1 π = 1 53360 640320 ∑ n = 0 ∞ (− 1) n (6 n)!

Ramanujan summation

Ramanujan Summation Formula Let f(z; ;q) := X1 k=1 qk 1 qk zk;z6= 0 : (1) We assume 0

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Ramanujan 1ψ1 summation ♦ 1—10 of 822 matching pages ♦ Search Advanced Help (0.005 seconds) 1—10 of 822 matching pages 1: 17.18 Methods of Computation …

Conclusion . Even though Ramanujan Summation was estimated as -1/12 by Euler and Ramanujan if it is . This might be compared to Heegner numbers, which have class number 1 and yield similar formulae. Ramanujan's series for π converges extraordinarily rapidly and forms the basis of some of the fastest algorithms currently used to calculate π.

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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… The Most Controversial Topic In Mathematics (Ramanujan Summation) Hello everyone!! Hope you all are well. Today, I am going to show you something that will blow your mind. 2017-09-13 And also in quantum mechanics(I know), Ramanujan summation is very important. Question.

Question. What is the value of Ramanujan summation in quantum mechanics? quantum-mechanics. Share.
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2019-09-27 · This equation doesn’t have a particular name as it has been proven by many mathematicians over the years while simultaneously being labeled a paradoxical equation. Now, to prove the Ramanujan Summation, we have to subtract the sequence ‘ C ‘ from the sequence ‘ B ‘.

× 13591409+545140134n 6403203n 1 π = 1 53360 640320 ∑ n = 0 ∞ (− 1) n (6 n)! n! 3 (3 n)!
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I Scientific American, februari 1988, finns en artikel om Ramanujan och π d¨ ar Summation motsvarar integration, och m˚ anga formler liknar varandra, t ex de

For Euler and Ramanujan it is just -1/12. Conclusion .

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)! n!3(3n)! × 13591409+545140134n 6403203n 1 π = 1 53360 640320 ∑ n = 0 ∞ (− 1) n (6 n)! n! 3 (3 n)! × 13591409 + 545140134 n 640320 3 n

Inom matematiken är Hardy-Ramanujans sats, bevisad av Ramanujan och Hardy 1917, Obviously something fishy is going on here, because an infinite sum of It's just that zeta regularization and Ramanujan summation is a bad 13.00-14.00 Eulers summation av 1-2+3-4+ Jockum 15.00-16.00 The man who knew infinity- om matematikern Srinavasa Ramanujan.

av M Krönika — (2) 94 (1971), 330–336. [24] Fefferman, C. A note on spherical summation multipliers. Ramanujan-Rademachers sats. Senare höll han också alla inringade A summeras och ger sannolikheten för att A vinner och (1+xx)^0.5 Euler (1773) 1+(3xx)/(10+(4-3xx)^0.5) Ramanujan (1914) Referee för The Ramanujan Journal.