Asymptotic estimates of sums involving the Moebius function
β Scribed by Krishnaswami Alladi
- Publisher
- Elsevier Science
- Year
- 1982
- Tongue
- English
- Weight
- 458 KB
- Volume
- 14
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
When studying the approximation of the wave functions of the \(H\)-atom by sums of Gaussians, Klopper and Kutzelnigg [KK] and Kutzelnigg [Ku] found an asymptotic of \(\exp [-\gamma \sqrt{n}]\). The results were obtained from numerical results and justified by some asymptotic expansions in quadrature
We give uniform estimates in the whole complex plane of entire functions of exponential type less than a certain numerical constant (approximately equal to 0.44) having sufficiently small logarithmic sums. In these estimates the entire dependence on the function is through its type and logarithmic s