Web1: MASTER TUNE ADJ. This is the DX27 MASTER TUNE function. All voices are affected simultaneously. The programmable data range is from -64 to +63. When set to 0, the … In analytic number theory, the Dickman function or Dickman–de Bruijn function ρ is a special function used to estimate the proportion of smooth numbers up to a given bound. It was first studied by actuary Karl Dickman, who defined it in his only mathematical publication, which is not easily available, and later … See more The Dickman–de Bruijn function $${\displaystyle \rho (u)}$$ is a continuous function that satisfies the delay differential equation $${\displaystyle u\rho '(u)+\rho (u-1)=0\,}$$ with initial conditions See more The main purpose of the Dickman–de Bruijn function is to estimate the frequency of smooth numbers at a given size. This can be used to … See more Friedlander defines a two-dimensional analog $${\displaystyle \sigma (u,v)}$$ of $${\displaystyle \rho (u)}$$. This function is used to estimate … See more • Broadhurst, David (2010). "Dickman polylogarithms and their constants". arXiv:1004.0519 [math-ph]. • Soundararajan, Kannan (2012). "An asymptotic expansion related to the … See more Dickman proved that, when $${\displaystyle a}$$ is fixed, we have $${\displaystyle \Psi (x,x^{1/a})\sim x\rho (a)\,}$$ See more For each interval [n − 1, n] with n an integer, there is an analytic function $${\displaystyle \rho _{n}}$$ such that See more • Buchstab function, a function used similarly to estimate the number of rough numbers, whose convergence to $${\displaystyle e^{-\gamma }}$$ is controlled by the … See more
Probability of being B smooth - Mathematics Stack Exchange
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Golomb-Dickman Constant -- from Wolfram MathWorld
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