Testwiki:Reference desk/Archives/Mathematics/2023 August 7

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August 7

Closeness of two (probably irrational) numbers

why are the number Catalan's constant and the number Γ(sr(3)) (where "sr" is principal square root and Γ(z) is the gamma function of variable z) differ by such very small percentage ? Are there any papers on mathematics have ever mentioned this stuff ? >>> i have found a related discussion of this stuff in mathstackexchange (https://math.stackexchange.com/questions/4670194/catalans-constant-unexpected-closeness) 2402:800:63AC:BE7D:D056:F908:8ED1:3853 (talk) 10:44, 7 August 2023 (UTC)

See Mathematical coincidence. I don't think one in a thousand is particularly special given that they use symbols that need looking up and theres a number of them. NadVolum (talk) 11:01, 7 August 2023 (UTC)

$\frac{\mathrm{\Gamma }(\frac{7}{12})-1}{\gamma }=0.9159647...$ is a lot closer, within $10^{-6}.$  --Lambiam 19:39, 7 August 2023 (UTC)