I am trying to solve this and Wolfram is giving me an answer of $b=18$ but I keep getting it down to a quadratic where I have to solve using the $-b$ formula and not getting the answer.
$$2b(b+1)\frac{\Gamma(b)}{\Gamma(b+3)} = 0.1$$
2026-04-07 11:09:48.1775560188
Solving for beta with gamma function
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You have
$$\Gamma(b+3) = (b+2)\Gamma(b+2) = (b + 2)(b + 1)\Gamma(b + 1) = (b + 2)(b + 1)b\Gamma(b),$$ so your equation becomes $$2b(b+1)\frac{1}{(b+2)(b + 1)b} = 0.1,$$ or $$\frac{2}{b + 2} = \frac{1}{10}.$$ This yields the linear equation $$b + 2 = 20,$$ so the solution is $b = 18$.