Mathematica package --- BRP

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Abstract:This Mathematica package computes the lower and upper bounds of the ratio of the partition functions.
For example, by the command

pnRatBound[2, z]

we get

{1 + (-((2 \[Pi]^2)/3) + \[Pi]^4/18)/z^2 + \[Pi]^2/(
  3 z), 80.8809/z^3, 66.1168/z^3, 30}

which means that for n > 30,

f(z) - 80.8809/z^3 < p(n+1)/p(n) < f(z) +  66.1168/z^3,

where

f(z) = 1 + (-((2 \[Pi]^2)/3) + \[Pi]^4/18)/z^2 + \[Pi]^2/(
  3 z)

and

z = mu(n) = Pi*Sqrt[24 n - 1]/6.

Translation or Not:no

CN No.:null