Results 21 to 30 of about 12,250,575 (319)
Sharp inequalities for the psi function and harmonic numbers [PDF]
Analysis, 2009 In the paper, two sharp inequalities for bounding the psi function ψ and the harmonic numbers Hn are established respectively, some known results are improved and some remarks are given.
Bai-Ni Guo (郭白妮), Feng Qi (祁锋)
semanticscholar +1 more source
Single and Double Knockouts of the Genes for Photosystem I Subunits G, K, and H of Arabidopsis [PDF]
, 2002 Photosystem I (PSI) of higher plants contains 18 subunits. Using Arabidopsis En insertion lines, we have isolated knockout alleles of the genes psaG, psaH2, and psaK, which code for PSI-G, -H, and -K.
Varotto, Claudio +7 more
core +1 more source
An inequality for generalized complete elliptic integral
Journal of Inequalities and Applications, 2017 In this paper, we show an elegant inequality involving the ratio of generalized complete elliptic integrals of the first kind and generalize an interesting result of Alzer.
Li Yin +3 more
doaj +1 more source
Improvements of the bounds for Ramanujan constant function
Journal of Inequalities and Applications, 2016 In the article, we establish several inequalities for the Ramanujan constant function R ( x ) = − 2 γ − ψ ( x ) − ψ ( 1 − x ) $R(x)=-2\gamma-\psi(x)-\psi(1-x)$ on the interval ( 0 , 1 / 2 ] $(0, 1/2]$ , where ψ ( x ) $\psi(x)$ is the classical psi ...
Hong-Hu Chu +3 more
doaj +1 more source
A class of completely monotonic functions involving the polygamma functions
Journal of Inequalities and Applications, 2022 Let Γ ( x ) $\Gamma (x)$ denote the classical Euler gamma function. We set ψ n ( x ) = ( − 1 ) n − 1 ψ ( n ) ( x ) $\psi _{n}(x)=(-1)^{n-1}\psi ^{(n)}(x)$ ( n ∈ N $n\in \mathbb{N}$ ), where ψ ( n ) ( x ) $\psi ^{(n)}(x)$ denotes the nth derivative of the
Li-Chun Liang, Li-Fei Zheng, Aying Wan
doaj +1 more source
Pauli graphs when the Hilbert space dimension contains a square: Why the Dedekind psi function? [PDF]
, 2010 We study the commutation relations within the Pauli groups built on all decompositions of a given Hilbert space dimension q, containing a square, into its factors.
M. Planat
semanticscholar +1 more source
Monotonicity and inequalities involving the incomplete gamma function
Journal of Inequalities and Applications, 2016 In the article, we deal with the monotonicity of the function x → [ ( x p + a ) 1 / p − x ] / I p ( x ) $x\rightarrow[ (x^{p}+a )^{1/p}-x]/I_{p}(x)$ on the interval ( 0 , ∞ ) $(0, \infty)$ for p > 1 $p>1$ and a > 0 $a>0$ , and present the necessary and ...
Zhen-Hang Yang, Wen Zhang, Yu-Ming Chu
doaj +1 more source
Padé approximant related to asymptotics for the gamma function
Journal of Inequalities and Applications, 2017 Based on the Padé approximation method, we determine the coefficients a j $a_{j}$ and b j $b_{j}$ ( 1 ≤ j ≤ k $1\leq j\leq k$ ) such that Γ ( x + 1 ) 2 π x ( x / e ) x = x k + a 1 x k − 1 + ⋯ + a k x k + b 1 x k − 1 + ⋯ + b k + O ( 1 x 2 k + 1 ) , x → ∞ ,
Xin Li, Chao-Ping Chen
doaj +1 more source
Cross sections for 2-to-1 meson–meson scattering
European Physical Journal C: Particles and Fields, 2021 We study the processes $$K{\bar{K}} \rightarrow \phi $$ K K ¯ → ϕ , $$\pi D \rightarrow D^*$$ π D → D ∗ , $$\pi {\bar{D}} \rightarrow {\bar{D}}^*$$ π D ¯ → D ¯ ∗ , and the production of $$\psi (3770)$$ ψ ( 3770 ) , $$\psi (4040)$$ ψ ( 4040 ) , $$\psi ...
Wan-Xia Li, Xiao-Ming Xu, H. J. Weber
doaj +1 more source
On some inequalities for the gamma and psi functions [PDF]
Mathematics of Computation, 1997 Summary: We present new inequalities for the gamma and psi functions, and we provide new classes of completely monotonic, star-shaped, and super-additive functions which are related to \(\Gamma\) and \(\psi\).
openaire +1 more source