Title of article
On the asymptotic representation of the Euler gamma function by Ramanujan
Author/Authors
Karatsuba، نويسنده , , Ekatherina A. Litvinova، نويسنده ,
Issue Information
روزنامه با شماره پیاپی سال 2001
Pages
16
From page
225
To page
240
Abstract
The problem of approximation to the Euler gamma function on the basis of some Ramanujanʹs formulas is considered. The function h(x)=(g(x))6−(8x3+4x2+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… .
Keywords
Euler gamma function , Asymptotic representation , Stirlingיs formulas , Monotonicity , Fourier series , Uniform estimate of the remainder , Lagrange formula
Journal title
Journal of Computational and Applied Mathematics
Serial Year
2001
Journal title
Journal of Computational and Applied Mathematics
Record number
1551552
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