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- W2007428802 abstract "Euler's constant 7 is defined to be the limit of the sequence as Ntends to infinity. This sequence converges rather slowly. We show how to accelerate the convergence by expanding the function f(x) = 1/xin a power series about each integral value x = nthen integrating term by term, and hence expressing the difference between 7 and γ(N) as a power series in 1/N, Evaluating the terms shown at N= 10 yields γ = 0.577 215 664 9... accurate to ten decimal places. Applying the same technique to f(x)= loge xwe establish Stirling's series for the factorial function. Approaching the sequence of functions f(x) =1/x k =2, 3,... in the same way yields similar series for the Riemann zeta function ζ(k)evaluated at k= 2,3,...." @default.
- W2007428802 created "2016-06-24" @default.
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- W2007428802 date "1997-09-01" @default.
- W2007428802 modified "2023-09-27" @default.
- W2007428802 title "Euler's constant, Stirling's approximation and the Riemann zeta function" @default.
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- W2007428802 doi "https://doi.org/10.1080/0020739970280504" @default.
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