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%I #23 Jun 27 2023 05:12:15
%S 5,0,3,7,5,5,9,1,4,1,8,0,1,5,6,0,1,7,9,1,6,8,6,1,9,0,1,4,5,8,2,7,1,4,
%T 6,5,6,3,7,2,1,2,7,0,3,7,7,4,4,3,0,9,9,4,6,8,1,8,7,0,4,0,0,5,6,0,1,1,
%U 4,4,5,0,5,3,5,8,8,0,2,1,3,5,4,4,3,0
%N Decimal expansion of ((3+2*5^(1/4))/(3-2*5^(1/4)))^(1/4).
%C Ramanujan's question 1070 (iii) asks for a proof of the identity
%C ((3+2*5^(1/4))/(3-2*5^(1/4)))^(1/4) = (5^(1/4)+1)/(5^(1/4)-1).
%C This is the larger of the two real roots of x^4 - 6*x^3 + 6*x^2 - 6*x + 1 = 0.
%D Srinivasa Ramanujan, Collected Papers, Chelsea, 1962, page 334, Question 1070.
%e 5.0375591418015601791686190145827146563721270377443099468187040056...
%t RealDigits[Surd[(3 + 2*5^(1/4))/(3 - 2*5^(1/4)), 4], 10, 120][[1]] (* _Amiram Eldar_, Jun 27 2023 *)
%o (PARI) ((3+2*5^(1/4))/(3-2*5^(1/4)))^(1/4)
%o (PARI) p(x)=x^4-6*x^3+6*x^2-6*x+1;
%o solve(x=5,6,p(x)) \\ _Hugo Pfoertner_, Sep 12 2018
%Y Cf. A318523, A318524.
%K nonn,cons
%O 1,1
%A _Hugo Pfoertner_, Aug 28 2018