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# Some New Algorithms for High-Precision Computation of Euler’s Constant

Chapter

## Abstract

We describe several new algorithms for the high-precision computation of Euler’s constant *γ* = 0.577.... Using one of the algorithms, which is based on an identity involving Bessel functions, *γ* has been computed to 30,100 decimal places. By computing their regular continued fractions we show that, if *γ* or exp(*γ*) is of the form *P/Q* for integers *P* and *Q*, then |*Q*| *>*10^{15000}

## Keywords

Asymptotic Expansion Continue Fraction Partial Quotient Precision Number Involve Bessel Function
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