SOME APPLICATIONS OF EXTENSION κ-GAMMA, κ-BETA FUNCTIONS AND k-BETA DISTRIBUTIONBapna, Indu BalaPrajapat, Radhe ShyamJournal of Ramanujan Society of Mathematics & Mathematical Sciences
In this paper, we first introduce the incomplete extended Gamma and Beta functions with matrix parameters; then, we establish some different properties for these new extensions. Furthermore, we give ...
We now apply our results to certain multiple Γ-type functions and multiple\log \Gamma-type functions that are known to be well-studied special functions, namely: the gamma function, the digamma function, the polygamma functions, theq-gamma function, the BarnesG-function, the Hurwitz zeta funct...
SL Qiu,M Vuorinen - 《Mathematics of Computation》 被引量: 98发表: 2004年 Some properties of the gamma and psi functions, with applications In this paper, some monotoneity and concavity properties of the gamma, beta and psi functions are obtained, from which several asymptotically sharp inequal...
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With the construction of the International Space Station, humans have been continuously living and working in space for 22 years. Microbial studies in space and other extreme environments on Earth have shown the ability for bacteria and fungi to adapt an
In semiconductor and data storage device manufacturing, it is desirable to produce feature sizes less than 30 nm with a high depth-to-width aspect ratio on the target material rapidly at a low cost. However, optical diffraction limits the smallest foc
Graphdiyne is a novel synthetic carbon-based nanomaterial withspandsp^{2}hybridized carbon atoms derived from acetylenic groups and benzene rings. This new material has been created by synthesizingsp^{2}andsp-hybridized carbon atoms15. The\alpha,\beta, and\gamma-type structures are the most notable...
Considering the realistic reconciliation efficiency, FER, and throughput, the SKR of the CV-QKD system can be expressed as: $$ {{K}_{\mathrm{prac}}}=\gamma (1-FER) (\beta {{I}_{AB}}-{{\chi }_{BE}}), $$ (2) where\(\gamma =P{{P}_{out}}/P{{P}_{in}}\),\(PP_{ou...