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 A129624 Decimal expansion of the constant x satisfying x! = Gamma[x+1] = 40. 3

%I

%S 4,3,3,1,2,9,2,4,2,4,4,9,9,7,1,3,4,6,5,8,3,8,9,4,1,4,9,1,0,4,2,3,3,8,

%T 0,8,1,1,3,8,5,6,1,5,4,6,0,2,6,7,8,2,2,9,7,2,8,7,4,9,9,5,5,7,4,8,5,7,

%U 5,2,1,7,4,7,9,4,1,7,3,7,6,1,4,6,8,8,2,7,5,2,1,3,3,9,2,4,4,1,5,3,3,9,4,5,1

%N Decimal expansion of the constant x satisfying x! = Gamma[x+1] = 40.

%C From symmetrical groups associated with exceptional groups: in this case the exceptional group now called E7.5. I call the symmetrical group S4_q. Solutions were provided in my egroup by Bob Hanlon and Peter Pein.

%F a(n) = nth_Digits[4.3312924244997134658389414910423380811385615460267822972874964374249]

%p read("transforms3") ; Digits := 120 ; x := 4.0 ; for l from 1 to 10 do x := x-(1-40/GAMMA(x+1))/Psi(x+1) ; x := evalf(x) ; end do; CONSTTOLIST(x) ; # _R. J. Mathar_, Mar 23 2010

%t (* Bob Hanlon (hanlonr(AT)cox.net): Solve is not intended for much beyond polynomial equations.Use FindRoot*) FindRoot[(4 + q)! - 40 == 0, {q, 0.5}] {q -> 0.3312924244997131`} FindRoot[Gamma[5 + q] - 40 == 0, {q, 0.5}] {q -> 0.3312924244997131`} (* Peter Pein : use the function FindRoot to get the zeros of transcendental functions :*) FindRoot[Gamma[5 + x] == 40, {x, 0, 1}, WorkingPrecision -> 50] {x -> 0.3312924244997134658389414910423380811385615460267822972874964374249` 49.99999999999999} FindRoot[(x + 4)! == 40, {x, 0, 1}, WorkingPrecision -> 50] {x -> 0.3312924244997134658389414910423380811385615460267822972874964374249` 49.99999999999999} (* digits from*) a = 0.3312924244997134658389414910423380811385615460267822972874964374249; Flatten[Join[{{4}}, Table[Mod[Floor[10^n*a], 10], {n, 1, 50}]]]

%K nonn,cons

%O 1,1

%A _Roger L. Bagula_, May 30 2007

%E More digits from _R. J. Mathar_, Mar 23 2010

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Last modified October 20 22:44 EDT 2019. Contains 328291 sequences. (Running on oeis4.)