Abstract
A new identity is given by means of which infinitely many algebraic functions approximating the logarithmic function In
x
are obtained. On substituting numerical algebraic values for the variable, a lower bound for the distance of its logarithm from variable algebraic numbers is found. As a further application, it is proved that the fractional part of the number e
a
is greater than
a
-40
a
for every sufficiently large positive integer
a
.
Cited by
41 articles.
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