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A129624
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Decimal expansion of the constant x satisfying x! = Gamma[x+1] = 40.
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3
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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, 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, 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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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4.331292424499713465838941491042338081138561546026782297287499557485752...
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MAPLE
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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
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MATHEMATICA
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(* 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}]]]
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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