On the asymptotic representation of the Euler gamma function by Ramanujan

By E. A. Karatsuba. 2001

80 citations recorded by the source corpus.

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−(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… .

Subfields: Algebra and Number Theory, Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/9e8ae3f58804d5fc9fb5e1302ae39d08d1cd1474

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In Algebra and Number Theory

1. Horst Alzer
2. Necdet Batır

In Applied Mathematics

1. Horst Alzer
2. Feng Qi (祁锋)
3. Bai-Ni Guo (郭白妮)
4. Necdet Batır
5. Y. Chu

Citations in the corpus

• On Ramanujan's Double Inequality for the Gamma Function (2003, background): “A short calculation reveals that (3.1) is equivalent to α f(x) β. (3.3) Applying Karatsuba’s monotonicity theorem, we get for x 1: α 0.0111 . . . = f(1) f(x) lim t→∞ f(t) = 1 30 .”