Abstract
The problem of approximation to the Euler gamma function on the basis of some Ramanujan's formulas is considered. The function h( x)=( g( x)) 6−(8 x 3+4 x 2+ x), where g(x)=(e/x) xΓ(1+x)/ π , is studied. It is proved that on the interval (1,∞) the function h( x) is increasing monotonically from h(1)=0.0111976… to h(∞)=1/30=0.0333… .
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