Some monotonicity properties and characterizations of the gamma function
β Scribed by Martin E. Muldoon
- Publisher
- Springer
- Year
- 1977
- Tongue
- English
- Weight
- 85 KB
- Volume
- 16
- Category
- Article
- ISSN
- 0001-9054
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π SIMILAR VOLUMES
## Abstract In this paper, we have exhibited, by utilizing value distribution theory, some new properties of the Gamma function Ξ(__z__) and the Riemann zeta function ΞΆ(__z__). Specifically, we have proved that both of the two functions are prime and the Riemann zeta function, like Ξ(__z__), does n
In this paper, conditions for matrices P, Q so that the Beta matrix function showing that hypotheses cannot be removed are also included. A limit expression for the Gamma function of a matrix is established.
The present knowledge of the monotonicity properties of the spherically averaged electron density p ( r ) and its derivatives, which comes mostly from Roothan-Hartree-Fock calculations, is reviewed and extended to all Hartree-Fock ground-state atoms from hydrogen ( Z = 1) to uranium ( Z = 92). In lo