On the asymptotic representation of the Euler gamma function by Ramanujan
| Autor: | Ekatherina A. Karatsuba |
|---|---|
| Rok vydání: | 2001 |
| Předmět: |
Monotonicity
Asymptotic representation Applied Mathematics Mathematical analysis Monotonic function Function (mathematics) Stirling's formulas Fourier series Ramanujan's sum Euler gamma function Combinatorics symbols.namesake Computational Mathematics Orthogonal polynomials symbols Lagrange formula Interval (graph theory) Stirling's approximation Uniform estimate of the remainder Gamma function Mathematics |
| Zdroj: | Journal of Computational and Applied Mathematics. 135(2):225-240 |
| ISSN: | 0377-0427 |
| DOI: | 10.1016/s0377-0427(00)00586-0 |
| Popis: | 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−(8x3+4x2+x), where g(x)=(e/x) x Γ(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… . |
| Databáze: | OpenAIRE |
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