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%I #17 Jan 29 2023 20:08:44
%S 9,8,2,6,0,9,8,2,5,0,1,3,2,6,4,3,1,1,2,2,3,7,7,4,8,0,5,6,0,5,7,4,9,1,
%T 0,9,4,6,5,3,8,0,9,7,2,4,8,9,9,6,9,4,4,3,0,0,6,3,9,9,3,6,2,1,9,2,8,9,
%U 1,5,8,2,5,1,5,5,0,2,7,1,9,3,4,4,9,4,2
%N Decimal expansion of Fibonorial(1/2).
%C This constant can be thought of as A003266(1/2).
%C The fibonorial of (not necessarily an integer) x is defined as x!_F = (phi^(x*(x+1)/2) / F(x+1)) * Product_{n=1..inf} F(n+1)^(x+1)/(F(n)^x * F(x+n+1)), where F(x) = (phi^x - cos(Pi*x)/phi^x)/sqrt(5), where phi = (1+sqrt(5))/2 is the golden ratio. It satisfies the recurrence 0!_F = 1, x!_F = (x-1)!_F * F(x), and agrees with A003266(x) at integer points.
%H Simon Plouffe, <a href="http://www.plouffe.fr/simon/constants/fibofact.txt">Fibonacci factorials</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Fibonorial.html">Fibonorial</a>, <a href="http://mathworld.wolfram.com/FibonacciFactorialConstant.html">Fibonacci Factorial Constant</a>.
%F Fibonorial(1/2) = phi^(3/8) * C / 5^(1/4), where C = A062073 is the Fibonacci factorial constant.
%e 0.98260982501326431122377480560574910946538...
%t RealDigits[N[GoldenRatio^(3/8) QPochhammer[-1/GoldenRatio^2]/5^(1/4), 100]][[1]]
%Y Cf. A003266, A062073.
%K nonn,cons
%O 0,1
%A _Vladimir Reshetnikov_, Sep 05 2016
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