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Revision History for A295872

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A295872

Decimal expansion of the first Ramanujan trigonometric constant (negated).
(history; published version)

#47 by N. J. A. Sloane at Sun Jul 15 12:06:27 EDT 2018

STATUS

proposed

approved

#46 by Michel Marcus at Sun Jul 15 02:29:38 EDT 2018

STATUS

editing

proposed

#45 by Michel Marcus at Sun Jul 15 02:29:30 EDT 2018

REFERENCES

B. C. Berndt, Y. S. Choi, S. Y. Kang, The problems submitted by Ramanujan to the Journal of Indian Math. Soc. in: Continued factions, fractions, Contemporary Math., 236 (1999), 15-56 (see Q524, JIMS VI, 1914).

STATUS

approved

editing

Discussion

Sun Jul 15

02:29

Michel Marcus: typo

#44 by Bruno Berselli at Thu Dec 14 04:45:27 EST 2017

STATUS

reviewed

approved

#43 by Peter Luschny at Thu Dec 14 03:40:39 EST 2017

STATUS

proposed

reviewed

#42 by Jon E. Schoenfield at Wed Dec 13 19:51:02 EST 2017

STATUS

editing

proposed

#41 by Jon E. Schoenfield at Wed Dec 13 19:50:59 EST 2017

COMMENTS

According to the famous Ramanujan identity, the constant r_1 has a representation: r_1 = Sum_{i = 1..3} (cos(2^i*Pi/7))^(1/3) (see formula). This identity was submitted in 1914 by Ramanujan as a problem (cf. [Berndt, Y. S. Choi, S. Y. Kang]). For proof, see first [V. Shevelev].

FORMULA

r_1 = ((5 - 3*7^(1/3))/2)^(1/3).

STATUS

proposed

editing

#40 by Peter Luschny at Wed Dec 13 16:16:18 EST 2017

STATUS

editing

proposed

#39 by Peter Luschny at Wed Dec 13 16:15:42 EST 2017

MAPLE

use RealDomain in solve(4*x^9 - 30*x^6 + 75*x^3 + 32 = 0) end use:

evalf(%, 79); # Peter Luschny, Dec 13 2017

STATUS

reviewed

editing

#38 by Robert G. Wilson v at Wed Dec 13 16:11:10 EST 2017

STATUS

proposed

reviewed